parameter induced stochastic resonance in an over damped linear system abstract stochastic resonance sr in an over damped linear system subjected to an excitation of bias signal modulated noise with multiplicative and additive noises is investigated we obtain the exact expressions of the first two moments and the signal to noise ratio snr of the output by using linear response theory the snr depends non monotonically on the intensity and the correlation time of multiplicative noise the correlation time of additive noise the intensity of the cross noise between multiplicative and additive noise as well as the external field frequency the conventional sr the sr in a broad sense and the bona fide sr are found in the system the influences of the asymmetries of multiplicative and additive noise the correlation rate of the cross noise the intensity of additive noise the amplitude of signal and the bias on the snr are analyzed moreover we pointed out that sr can be realized by tuning the system parameter with fixed noise i e parameter induced stochastic resonance psr exists

beyond the fokker planck equation pathwise control of noisy bistable systems we introduce a new method allowing one to describe slowly time dependent langevin equations through the behaviour of individual paths this approach yields considerably more information than the computation of the probability density in particular scaling laws can be obtained easily the main idea is to show that for sufficiently small noise intensity and slow time dependence the vast majority of paths remain in small space time sets typically in the neighbourhood of potential wells the size of these sets often has a power law dependence on the small parameters with universal exponents the overall probability of exceptional paths is exponentially small with an exponent also showing power law behaviour the results cover time spans up to the maximal kramers time of the system we apply our method to three phenomena characteristic for bistable systems stochastic resonance dynamical hysteresis and bifurcation delay where it yields precise bounds on transition probabilities and the distribution of hysteresis areas and first exit times we also discuss the effect of coloured noise

receiver operating characteristic curves for a simple stochastic process that carries a static signal the detection of a weak signal in the presence of noise is an important problem that is often studied in terms of the receiver operating characteristic roc curve in which the probability of correct detection is plotted against the probability for a false positive this kind of analysis is typically applied to the situation in which signal and noise are stochastic variables the detection problem emerges however also often in a context in which both signal and noise are stochastic processes and the correct or false detection is said to take place when the process crosses a threshold in a given time window here we consider the problem for a combination of a static signal which has to be detected against a dynamic noise process the well known ornstein uhlenbeck process we give exact but difficult to evaluate quadrature expressions for the detection rates for false positives and correct detections investigate systematically a simple sampling approximation suggested earlier compare to an approximation by stratonovich for the limit of high threshold and briefly explore the case of multiplicative signal all theoretical results are compared to extensive numerical simulations of the corresponding langevin equation our results demonstrate that the sampling approximation provides a reasonable description of the roc curve for this system and it clarifies limit cases for the roc curve

control of noise induced oscillations by delayed feedback abstract we propose a method to control noise induced motion based on using delayed feedback in the form of the difference between the delayed and the current states of the system the method is applied to two different types of systems namely a self oscillator near andronov hopf bifurcation and a threshold system in both cases we demonstrate that by variation of time delay one can effectively control coherence and timescales of stochastic oscillations the entrainment of the basic period of oscillations by time delay is discovered we give explanations of the phenomena observed and provide a theory for the system near bifurcation

stochastic resonance in a tunnel diode we study stochastic resonance in a fast bistable electronic system a tunnel diode we investigate the phenomenon in a higher frequency regime than that studied in previous experiments detailed measurements of the output signal are reported for two values of the frequency of the periodic signal mathit f mathit s 1 khz and mathit f mathit s 10 khz we observe in one case mathit f mathit s 1 khz a nonmonotonic behavior characterized by a sharp dip in the output noise level measured at the frequency of the driving signal

stochastic resonance in chaotic systems the phenomenon of stochastic resonance sr is investigated for chaotic systems perturbed by white noise and a harmonic force the bistable discrete map and the lorenz system are considered as models it is shown that sr in chaotic systems can be realized via both parameter variation in the absence of noise and by variation of the noise intensity with fixed values of the other parameters

stochastic resonance of electrochemical aperiodic spike trains aperiodic stochastic resonance in an electrochemical system with excitable dynamics is characterized in experiments and simulations two different spike trains one with stochastic and the other with chaotic interspike intervals are imposed on the system as subthreshold aperiodic signals information transmission is quantified by the cross correlation between the subthreshold input signal and the noise induced system response a maximum is exhibited in the input output correlation as a function of the noise amplitude numerical simulations with an electrochemical model are in excellent agreement with the experimental observations

multifractal characterization of stochastic resonance we use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals to characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence we use wavelet transform modulus maxima method for the singularity spectrum computations it is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic stochastic or chaotic input signals we show that in the case of periodic driving force singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization this fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also moreover our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence we use also the proposed approach to characterize the noise enhanced dynamics of a coupled stochastic neurons model

free vibrations of a mono coupled periodic system abstract vibration problems of periodic systems can be analyzed efficiently by means of the transfer matrix method the frequency equation for the whole system is shown to be obtained in terms of the eigenvalues or their natural logarithms which are often called propagation constants of the transfer matrix for a single periodic subsystem in case of a mono coupled system this frequency equation may be solved graphically by using the propagation constant curve thereby saving a great deal of computational effort two types of mono coupled systems are considered as numerical examples a spring mass oscillating system and a continuous timoshenko beam resting on regularly spaced knife edge supports depending on whether the transfer matrix is derived by an analytical procedure or by the finite element method the numerical solutions become either exact or approximate

stochastic resonance in overdamped two coupled anharmonic oscillators abstract we consider the overdamped version of two coupled anharmonic oscillators with the external periodic force f sin t and gaussian noise term t added to one of the two state variables of the system linear stability analysis is carried out in the absence of external periodic force and noise then the system with external periodic force only and noise term only are studied in the noise free system four period t orbits are found to co exist one in each of the four wells for small values of forcing amplitude f for fixed values of other parameters at a critical value of f f c cross well periodic orbit appears f c is found to increase with increase in the coupling strength in the absence of forcing the system is found to exhibit intermittent jumping motion between two wells above a particular value of noise strength d d c the noise induced jumping behaviour is characterized by first passage time and residence time distributions next the influence of noise in the presence of the external periodic force is numerically studied the system is found to exhibit stochastic resonance behaviour the observed stochastic resonance dynamics is characterized using power spectrum signal to noise ratio and residence time distribution the plot of maximal lyapunov exponent versus noise strength has shown a stochastic resonance profile the occurrence of stochastic resonance is studied by varying the forcing frequency and the coupling strength finally the influence of addition of external periodic force and noise term to different state variables is also presented

frequency analysis of tick quotes on foreign currency markets and the double threshold agent model abstract power spectrum densities for the number of tick quotes per minute market activity on three currency markets usd jpy eur usd and jpy eur are analyzed for periods from january 2000 to december 2000 we find some peaks on the power spectrum densities at a few minutes we develop the double threshold agent model and confirm that the corresponding periodicity can be observed for the activity of this model even though market participants perceive common weaker periodic information than threshold for decision making of them this model is numerically performed and theoretically investigated by utilizing the mean field approximation we propose a hypothesis that the periodicities found on the power spectrum densities can be observed due to nonlinearity and diversity of market participants

dynamical behaviors of inter out of equilibrium state intervals in korean futures exchange markets a recently discovered feature of financial markets the two phase phenomenon is utilized to categorize a financial time series into two phases namely equilibrium and out of equilibrium states for out of equilibrium states we analyze the time intervals at which the state is revisited the power law distribution of inter out of equilibrium state intervals is shown and we present an analogy with discrete time heat bath dynamics similar to random ising systems in the mean field approximation this model reduces to a one dimensional multiplicative process by varying global and local model parameters the relevance between volatilities in financial markets and the interaction strengths between agents in the ising model are investigated and discussed

stochastic resonance in a stochastic bistable system subject to additive white noise and dichotomous noise abstract the stochastic resonance sr in a stochastic stable system driven by a static force and a periodic square wave signal as well as by additive white noise and dichotomous noise is considered from the point of view of the signal to noise ratio snr it is found that the snr exhibits sr behavior when it is plotted as a function of the noise strength of the white noise and dichotomous noise as well as when plotted as a function of the static force moreover the influence of the strength of the stochastic potential force and the correlation rate of the dichotomous noise is investigated

wavelet transform analysis of time series generated by the stimulated neuronal activity abstract we have studied the stimulated discharge dynamics of fusimotor neurons by applying the wavelet transform technique and by adopting that the neuronal discharge dynamics is manifested by the random time series of interspike intervals we found two different power law type behaviors along interspike intervals isi time scale which implies existence of two different types of neuronal noise which are separated by a crossover region our results reveal that complex neuronal dynamics in the presence of external stimulation is manifested with long range correlated noise in the region before the crossover on the isi time scale

stochastic resonance in periodic potentials the phenomenon of stochastic resonance sr is known to occur mostly in bistable systems however the question of the occurrence of sr in periodic potential systems has not been resolved conclusively our present numerical work shows that the periodic potential system indeed exhibits sr in the high frequency regime where the linear response theory yields maximum frequency dependent mobility as a function of noise strength the existence of two and only two distinct dynamical states of trajectories in this moderately feebly damped periodically driven noisy periodic potential system plays an important role in the occurrence of sr

short time fourier transform using a bank of low pass filters the purpose of this paper is to present some experimental results estimating instantaneous frequencies of fm frequency modulation signals using the short time fourier transform stft method the relevant stft coefficients were computed using a bank of simple one pole low pass filters which estimates the cross correlation of a given signal and complex sinusoids also it is shown that computing the stft coefficients is equivalent to finding the least square solution which best approximates the given signal as a weighted sum of complex sinusoids

stochastic resonance in coupled threshold elements on a barabasi albert network abstract stochastic resonance is investigated in a system of threshold elements located at nodes and coupled along edges of a barabasi albert network driven by a common subthreshold periodic signal and independent noises array enhanced stochastic resonance is observed i e increase of the spectral power amplification evaluated from the mean output of the network due to proper coupling this enhancement occurs though the response of individual threshold elements to the periodic signal is very diverse due to a power law distribution of their connectivity numerical results are qualitatively explained using simple linear response theory in the mean field approximation

stochastic resonance in monostable systems the first observations of noise induced enhancements and phase shifts of a weak periodic signal characteristics signatures of stochastic resonance sr are reported for a monostable system the results are shown to be in good agreement with a theoretical description based on linear response theory and the fluctuation dissipation theorem it is argued that sr is a general phenomenon that can in principle occur for any underdamped nonlinear oscillator

multiple cross correlation noise induced transition in a stochastic bistable system abstract based on the stochastic equivalent rules the fokker planck equation for a general one dimensional nonlinear system subjected to n component noises and cross correlation noises is derived and the greatest advantage of the method lies in its simplicity applying this method the effects of multiple sources of noise and the correlation forms of noises among them i e two multiplicative noises an additive noise and the correlation between the three noises on the steady state properties and the mean first passage time mfpt of a stochastic bistable system are discussed in details the results show rich transition phenomena such as the reentrance like noise induced phenomenon and the switch between the bimodal and the unimodal structure for different noise intensities moreover the effects of the cross correlation among the three noise sources on the mfpt are also discussed and the noise enhanced stability phenomenon and the resonant activation phenomenon are observed the numerical results are in basic agreement with the theoretical predictions

stochastic resonance in a linear system an exact solution multistable systems can exhibit stochastic resonance which is characterized by the amplification of small periodic signals by additive noise here we consider a nonmultistable linear system with a multiplicative noise forced by an external periodic signal the noise is the sum of a colored noise of mean value zero and a noise with a definite sign we show that the system exhibits stochastic resonance through the numerical study of an exact analytical expression for the mean value obtained by functional integral techniques this is proof of the effect for a very general kind of noise which can even have a definite sign

solving langevin equation with the bicolour rooted tree method national basic research program of china 973 program 2007cb814800 national natural science foundation of china 10475067

effect of asymmetry on stochastic resonance and stochastic resonance induced by multiplicative noise and by mean field coupling in the paper we investigate the effect of asymmetry of the potential on stochastic resonance sr for a model with an asymmetric bistable potential and driven by additive noise the signal to noise ratio snr for a model with a monostable potential and driven by additive and multiplicative noises and the snr for a mean field coupled model with infinite globally coupling oscillators driven by additive noises it is shown that for the first model the asymmetry of the potential can weaken the phenomenon of sr for the second and third models a sr induced by multiplicative noise and a different one caused by mean field coupling are found

invariant representation of propagation properties for bi coupled periodic structures general bi coupled periodic systems are dealt with by means of transfer matrices of single units the solutions of the associated characteristic equation are discussed in terms of invariant quantities by exploiting the well known reversibility of its coefficients an exhaustive description of the free wave propagation patterns is given on the invariant plane where propagation domains with qualitatively different character are identified the asymptotic behavior of the roots of the characteristic equation when the invariants tend to infinity is analyzed the contour plot of the real part of the propagation constants responsible for the amount of attenuation of the characteristic waves is illustrated on the invariants plane next several models of bi coupled periodic structures made up of beams resting on elastic supports are considered a non linear mapping from the invariants plane to the physical parameters plane provides a concise representation of the pattern of the propagation domains a mechanical interpretation associated with the boundaries of these regions is given finally the proper selection of the physical parameters governing the propagation modes is discussed

correlation anti correlation transition by state dependent poisson noise noise may induce some degrees of order in many biological and complex systems we present an example of a noise dependent transition from correlation to anti correlation of the states of a bivariate system coupled by state dependent poisson noises by varying the degree of dependence of the rate of jumps on the other variable the system undergoes different degrees of correlation from independence to perfect correlation which in this case coincides with perfect synchronization in the limit of the deterministic periodic case

stochastic resonance in a linear fractional langevin equation the fractional langevin equation is derived from the generalized langevin equation driven by the additive fractional gaussian noise we investigate the stochastic resonance sr phenomenon in the underdamped linear fractional langevin equation under the external periodic force and multiplicative symmetric dichotomous noise applying the shapiro loginov formula and the laplace transform technique we obtain the exact expressions of the amplitude and signal to noise ratio snr of the system by studying the impacts of the driving frequency and the noise parameters we find the non monotonic behaviors of the output amplitude and snr the results indicate that the bona fide sr conventional sr and the wide sense of sr phenomena occur in the proposed linear fractional system

characterization of subthreshold voltage fluctuations in neuronal membranes synaptic noise due to intense network activity can have a significant impact on the electrophysiological properties of individual neurons this is the case for the cerebral cortex where ongoing activity leads to strong barrages of synaptic inputs which act as the main source of synaptic noise affecting on neuronal dynamics here we characterize the subthreshold behavior of neuronal models in which synaptic noise is represented by either additive or multiplicative noise described by ornstein uhlenbeck processes we derive and solve the fokker planck equation for this system which describes the time evolution of the probability density function for the membrane potential we obtain an analytic expression for the membrane potential distribution at steady state and compare this expression with the subthreshold activity obtained in hodgkin huxley type models with stochastic synaptic inputs the differences between multiplicative and additive noise models suggest that multiplicative noise is adequate to describe the high conductance states similar to in vivo conditions because the steady state membrane potential distribution is easily obtained experimentally this approach provides a possible method to estimate the mean and variance of synaptic conductances in real neurons

stochastic resonance in linear systems subject to multiplicative and additive noise exact expressions have been found for the first two moments and the correlation function for an overdamped linear system subject to an external periodic field as well as to multiplicative and additive noise stochastic resonance is absent for gaussian white noise however when the multiplicative noise has the form of an asymmetric dichotomous noise the signal to noise ratio snr becomes a nonmonotonic function of the correlation time and the asymmetry of noise moreover the snr turns out to be a nonmonotonic function of the frequency of the external field as well as strongly depending on the strength of the cross correlation between multiplicative and additive noise

stochastic resonance in a trapping overdamped monostable system the response of a trapping overdamped monostable system to a harmonic perturbation is analyzed in the context of stochastic resonance phenomenon we consider the dynamics of a brownian particle moving in a piecewise linear potential with a white gaussian noise source based on linear response theory and laplace transform technique analytical expressions of signal to noise ratio snr and signal power amplification spa are obtained we find that the snr is a nonmonotonic function of the noise intensity while the spa is monotonic theoretical results are compared with numerical simulations

a model for prejudiced learning in noisy environments based on the heuristics that maintaining presumptions can be beneficial in uncertain environments we propose a set of basic requirements for learning systems to incorporate the concept of prejudice the simplest memoryless model of a deterministic learning rule obeying the axioms is constructed and shown to be equivalent to the logistic map the system s performance is analysed in an environment in which it is subject to external randomness weighing learning defectiveness against stability gained the corresponding random dynamical system with inhomogeneous additive noise is studied and shown to exhibit the phenomena of noise induced stability and stochastic bifurcations the overall results allow for the interpretation that prejudice in uncertain environments can entail a considerable portion of stubbornness as a secondary phenomenon

correlated noise in a logistic growth model the logistic differential equation is used to analyze cancer cell population in the presence of a correlated gaussian white noise we study the steady state properties of tumor cell growth and discuss the effects of the correlated noise it is found that the degree of correlation of the noise can cause tumor cell extinction

resonant behavior of a fractional oscillator with fluctuating frequency the long time behavior of the first moment for the output signal of a fractional oscillator with fluctuating frequency subjected to an external periodic force is considered colored fluctuations of the oscillator eigen frequency are modeled as a dichotomous noise the viscoelastic type friction kernel with memory is assumed as a power law function of time using the shapiro loginov formula exact expressions for the response to an external periodic field and for the complex susceptibility are presented on the basis of the exact formulas it is demonstrated that interplay of colored noise and memory can generate a variety of cooperation effects such as multiresonances versus the driving frequency and the friction coefficient as well as stochastic resonance versus noise parameters the necessary and sufficient conditions for the cooperation effects are also discussed particularly two different critical memory exponents have been found which mark dynamical transitions in the behavior of the system

processing of acoustic waveforms a sinusoidal model for acoustic waveforms is applied to develop a new analysis synthesis technique which characterizes a waveform by the amplitudes frequencies and phases of component sine waves these parameters are estimated from a short time fourier transform rapid changes in the highly resolved spectral components are tracked using the concept of birth and death of the underlying sine waves the component values are interpolated from one frame to the next to yield a representation that is applied to a sine wave generator the resulting synthetic waveform preserves the general waveform shape and is perceptually indistinguishable from the original furthermore in the presence of noise the perceptual characteristics of the waveform as well as the noise are maintained the method and devices disclosed herein are particularly useful in speech coding time scale modification frequency scale modification and pitch modification

the availability of logical operation induced by dichotomous noise for a nonlinear bistable system instead of a continuous system driven by gaussian white noise logical stochastic resonance will be investigated in a nonlinear bistable system with two thresholds driven by dichotomous noise which shows a phenomenon different from gaussian white noise we can realize two parallel logical operations by simply adjusting the values of these two thresholds besides to quantify the reliability of obtaining the correct logic output we numerically calculate the success probability and effects of dichotomous noise on the success probability are observed these observations show that the reliability of realizing logical operation in the bistable system can be improved through optimizing parameters of dichotomous noise

concept of complexity in random dynamical systems we introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system in dynamical systems with small random perturbations this indicator coincides with the rate k of divergence of nearby trajectories evolving under two different noise realizations the meaning of k is discussed in the context of the information theory and it is shown that it can be determined from real experimental data in the presence of strong dynamical intermittency the value of k is very different from the standard lyapunov exponent ensuremath lambda mathrm ensuremath sigma computed considering two nearby trajectories evolving under the same realization of the randomness however the former is much more relevant than the latter from a physical point of view as illustrated by some numerical computations for noisy maps and sandpile models textcopyright 1996 the american physical society

stochastic resonance in linear system driven by multiplicative and additive noise abstract the stochastic resonance sr is studied in an overdamped linear system driven by multiplicative and additive noise when the additive noise is a linear combination of an asymmetric dichotomous noise and its square the exact expressions are obtained for the first two moments and the correlation function and the sr phenomenon appeared there are three different forms of sr the bona fide sr the conventional sr and sr in the broad sense moreover the asymmetry of multiplicative noise has different effect on signal to ratio snr for the first two different forms of sr and the effects of multiplicative noise and additive noise on snr are different

relation between optimal nonlinearity and non gaussian noise enhancing a weak signal in a nonlinear system in the study of stochastic resonance it is often mentioned that nonlinearity can enhance a weak signal embedded in noise in order to give a systematic proof of the signal enhancement in nonlinear systems we derive an optimal nonlinearity that maximizes a signal to noise ratio snr the obtained optimal nonlinearity yields the maximum unbiased signal estimation performance which is known in the context of information theory it is found that a linear system is optimal for a gaussian noise but for a non gaussian noise there exist nonlinear systems that can achieve an snr higher than that obtained from linear systems this analysis refers to a system subjected to an additive non gaussian noise with a small signal input

vibration reduction in piecewise bi coupled periodic structures the problem of minimizing transmitted vibrations through finitely long periodic structures is addressed bi coupled periodic element properties and arrangement are tailored to localize the response around the excitation source within any assigned frequency range bi dimensional analytical maps of the single unit free wave propagation domains stop pass and complex domains provide the optimal choice of the cell properties and ordering moreover the amount of vibration suppression along the periodic structure is also controlled as it can be described through iso attenuation curves representing the contour plot of the real part of the propagation constants applications to both undamped and damped beams resting on elastic supports are illustrated the response of the periodic structures to harmonic excitations is expressed through the wave vector method taking into account the effects of wave reflection due to changes in the cell properties along the structure and boundary conditions such computational schemes enables one to overcome numerical difficulties arising in the transfer matrix formulation for structures with a large number of periodic units

effect of correlated dichotomous noises on stochastic resonance in a linear system a linear system driven by correlated asymmetric dichotomous noises and periodic signal was investigated in the overdamped case the exact expressions of output signal amplitude and signal to noise ratio snr of the system were derived by means of numerical calculations we found that i at some fixed multiplicative noise intensities the output signal amplitude with frequency exhibits the structure of a weak peak even no peak as the dichotomous noise is asymmetric ii in the case of asymmetric dichotomous noise the signal frequency can cause non monotonous behavior of the output signal amplitude with respect to multiplicative noise intensity iii the curve of snr with frequency has a weak peak and a trough in the case of symmetric dichotomous noise but no peak with asymmetric iv whether the multiplicative noise is symmetric or asymmetric the noise can enhance response of the system v the snr increases with the correlation strength between the two noises decreasing in addition the plane of multiplicative noise intensity versus noise symmetric parameter was plotted

optimal weighted suprathreshold stochastic resonance with multigroup saturating sensors abstract suprathreshold stochastic resonance ssr describes a noise enhanced effect that occurs not in a single element but rather in an array of nonlinear elements when the signal is no longer subthreshold within the context of ssr we investigate the optimization problem of signal recovery through an array of saturating sensors where the response of each element can be optimally weighted prior to summation with a performance measure of mean square error mse we consider groups of sensors individual sensors within each group have identical parameters but each group has distinct parameters we find that optimally weighting the sensor responses provides a lower mse in comparison with the unweighted case for weak and moderate noise intensities moreover as the slope parameter of the nonlinear sensors increases the mse superiority of the optimally weighted array shows a peak and then tends to a fixed value these results indicate that ssr with optimal weights as a general mechanism of enhancement by noise is of potential interest to signal recovery

theory of the stochastic resonance effect in signal detection part ii variable detectors in part i of this paper ldquotheory of the stochastic resonance effect in signal detection part i fixed detectors rdquo ieee transactions on signal processing vol 55 no 7 pt 1 pp 3172 3184 the mechanism of the stochastic resonance sr effect for a fixed detector has been examined this paper analyzes the stochastic resonance sr effect under the condition that the detector structure or its parameters can also be changed the detector optimization problem with sr noise under both neyman pearson and bayesian criteria is examined in the bayesian approach when the prior probabilities are unknown the minimax approach is adopted the form of the optimal noise pdf along with the corresponding detector as well as the maximum achievable performance are determined the developed theory is then applied to a general class of weak signal detection problems under the assumptions that the sample size n is large enough and the test statistics satisfies the conditions of central limit theorem the optimal sr noise is shown to be a constant vector and independent of the signal strength for both neyman pearson and bayesian criteria illustrative examples are presented where performance comparisons are made between the original detector and the optimal sr noise modified detector for different types of sr noise

linear transmitter with correlated noises abstract a linear transmitter with correlated gaussian white additive and multiplicative noises and a periodic signal coupled either additively or multiplicatively is considered the correlations have a weak destructive effect in case of the additive signal and a strong constructive effect in case of the multiplicative one analytical results for the linear transmitter with the additive signal agree with those obtained previously by a different approach we also show how to analytically calculate certain expectation values involving exponentials of gaussian processes

stochastic resonance in an ensemble of bistable systems under stable distribution noises and nonhomogeneous coupling in this paper stochastic resonance of an ensemble of coupled bistable systems driven by noise having an stable distribution and nonhomogeneous coupling is investigated the stable distribution considered here is characterized by four intrinsic parameters 0 2 is called the stability parameter for describing the asymptotic behavior of stable densities 1 1 is a skewness parameter for measuring asymmetry 0 is a scale parameter for measuring the width of the distribution and is a location parameter for representing the mean value it is demonstrated that the resonant behavior is optimized by an intermediate value of the diversity in coupling strengths we show that the stability parameter and the scale parameter can be well selected to generate resonant effects in response to external signals in addition the interplay between the skewness parameter and the location parameter on the resonance effects is also studied we further show that the asymmetry of a l evy stable distribution resulting from the skewness parameter and the location parameter can enhance the resonance effects both theoretical analysis and simulation are presented to verify the results of this paper

wave propagation in three coupled periodic structures free wave propagation patterns for general three coupled periodic structures are investigated by means of the transfer matrix approach it is shown that an exhaustive description of the propagation domains requires spaces that are stratified in homogeneous regions whose dimension is given by the number of invariants of the transfer matrix characteristic equation and whose boundaries are represented by codimension one manifolds three types of three coupled periodic mechanical models characterized by constitutive elastic and or inertial coupling between mono and bi coupled dynamics namely pipes thin walled beams and truss beams are considered from the design standpoint an adequate representation of the propagation domains pattern is obtained through a nonlinear mapping from the space of the invariants to the physical parameters plane the analyzed models give rise to equations of motion where the three coupled nature stems from the coupling between transversal bi coupled and longitudinal mono coupled dynamics for the pipes and truss beams whilst coupling occurs between transversal and torsional mono coupled dynamics when it comes to the thin walled beams a mechanical interpretation associated with the bounding frequencies of the propagation regions is given and the evolution of the propagation properties when coupling parameters tend to vanish is discussed

parameter induced aperiodic stochastic resonance in the presence of multiplicative noise and additive noise abstract parameter induced aperiodic stochastic resonance sr in the presence of multiplicative and additive noise is investigated in detail using theoretical and numerical analysis we evaluate the dynamical probability density by which the bit error rate is defined as a quantity to optimize in the aperiodic sr problem via tuning the system parameters tuning the system parameters includes two cases one is parameter optimized and the other is parameter induced sr to distinguish them we use the conventional method in which sr is realized by varying the noise intensity essentially parameter induced sr is based on the cooperative effect between the stochastic subjected dynamical system and the input signal by changing the intrinsic characteristic of the nonlinear system via tuning the system parameters rather than by adding noise the theory is tested against numerical simulations

stochastic resonance in a mono stable system with multiplicative and additive noise the stochastic resonance in a biased mono stable system subject to multiplicative and additive noise is investigated based on the adiabatic approximation theory the analytic expression of the signal to noise ratio snr is obtained it is shown that the snr is a non monotonic function of the intensities of the multiplicative and additive noise as well as the parameters of the mono stable system

influence of delayed time and colored noise in a bistable system subject to asymmetric dichotomous noise and colored noise the influence of delayed time and colored noise in a bistable system subject to asymmetric dichotomous noise and colored noise is studied applying small delay time approximation under the adiabatic limit condition the expression of the signal to noise ratio snr of the system is obtained it is found that the snr varies non monotonously with the delayed time and the correlation of the colored noise moreover the snr exhibits sr behavior when it is plotted as a function of the intensity and asymmetry of the dichotomous noise and as a function of the strength of the colored noise

stochastic resonance in an activator inhibitor system through adiabatic and quasi variational approaches abstract we study the phenomenon of stochastic resonance in a spatially extended system an activator inhibitor reaction diffusion model is analyzed through two different approximations an adiabatic one leading to a known form of the graham s nonequilibrium potential and a quasi variational approach that allows to obtain an approximated form of graham s potential for a different parameter region those potentials have been exploited to obtain firstly the probability for the decay of the metastable extended states and secondly expressions for the correlation function and for the signal to noise ratio within the framework of a two state description the analytical results show how this ratio depends on both local and nonlocal coupling parameters

properties of diffusive systems near a saddle point application to a quartic double well this paper aims at the analysis of diffusive properties of unidimensional mechanical systems in the environment of maxima and minima of the potential it begins with a study of the properties of the singular solutions of the hamilton jacobi yasue equation in the above mentioned environment in both strong or very small frictional forces for the quartic symmetrical double well potential approximate solutions are found for local validity and the diffusion operator is then calculated in the limits of deep wells and small temperature the regime being supposed to be aperiodic with high or moderate values of frictional coefficient this equation is proved to be nonunique this operator is then reduced to second order by imposing suitable boundary conditions thus an appropriate eigenvalue equation is obtained to describe stationary states in the environment of extremal points of the potential energy function the main interest of this work relies upon the fact that transition times between wells mainly depend upon fluctuations near the saddle point

time scale and noise optimality in self organized critical adaptive networks recent studies have shown that adaptive networks driven by simple local rules can organize into critical global steady states providing another framework for self organized criticality soc we focus on the important convergence to criticality and show that noise and time scale optimality are reached at finite values this is in sharp contrast to the previously believed optimal zero noise and infinite time scale separation case furthermore we discover a noise induced phase transition for the breakdown of soc we also investigate each of these three effects separately by developing models that reveal three generically low dimensional dynamical behaviors time scale resonance a simplified version of stochastic resonance which we call steady state stochastic resonance and noise induced phase transitions

stochastic resonance in a fractional harmonic oscillator subject to random mass and signal modulated noise stochastic resonance in a fractional harmonic oscillator with random mass and signal modulated noise is investigated applying linear system theory and the characteristics of the noises the analysis expression of the mean output amplitude gain oag is obtained it is shown that the oag varies non monotonically with the increase of the intensity of the multiplicative dichotomous noise with the increase of the frequency of the driving force as well as with the increase of the system frequency in addition the oag is a non monotonic function of the system friction coefficient as a function of the viscous damping coefficient as a function of the fractional exponent

the green kubo formula and power spectrum of reversible markov processes as is known the entropy production rate of a stationary markov process vanishes if and only if the process is reversible in this paper we discuss the reversibility of a stationary markov process from a functional analysis point of view it is shown that the process is reversible if and only if it has a symmetric markov semigroup equivalently a self adjoint infinitesimal generator applying this fact we prove that the green kubo formula holds for reversible markov processes by demonstrating that the power spectrum of each reversible markov process is lorentz typed we show that it is impossible for stochastic resonance to occur in systems with zero entropy production

stochastic resonance in deterministic chaotic systems we propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems it is shown that even in the absence of noise when the control parameter changes periodically in time below and above the threshold for the onset of chaos stochastic resonance effects appear as a result one has an alternation of chaotic and regular i e predictable evolutions in an almost periodic way so that the lyapunov exponent is positive but some time correlations do not decay

noise benefits in combined nonlinear bayesian estimators this paper investigates the benefits of intentionally adding noise to a bayesian estimator which comprises a linear combination of a number of individual bayesian estimators that are perturbed by mutually independent noise sources and multiplied by a set of adjustable weighting coefficients we prove that the bayes risk for the mean square error mse criterion is minimized when the same optimum weighting coefficients are assigned to the identical estimators in the combiner this property leads to a simplified analysis of the noise benefit to the mse of the combined bayesian estimator even when the number of individual estimators tends to infinity it is shown that for a sufficiently large number of individual estimators the mse of the designed bayesian estimator approaches a plateau for a wide range of added noise levels this robust feature facilitates the incorporation of the added noise into the design of bayesian estimators without tuning the noise level for an easily implementable bayesian estimator composed of quantizers the benefit of the symmetric scale family noise is demonstrated and the optimal noise probability density function is approximated by solving a constrained nonlinear optimization problem we further extend this potential bayesian estimator to the nonlinear filter design finally examples of the noise benefits in random parameter estimation and nonlinear filtering support the theoretical analyses

stochastic resonance driven by two different kinds of colored noise in a bistable system the phenomenon of stochastic resonance in a bistable nonlinear system is investigated when both the multiplicative noise and the coupling between additive and multiplicative noise are colored with different values of noise correlation time ensuremath tau 1 and ensuremath tau 2 combining the functional analysis and unified colored noise approximation the two different kinds of colored noise in the nonlinear system can be simplified the signal to noise ratio is calculated when a weakly periodic signal is added to the system it is found that there appears a transition between one peak and two peaks in the curve of the signal to noise ratio when either the noise correlation time ensuremath tau 1 and ensuremath tau 2 or the coupling strength ensuremath lambda between additive and multiplicative noise is increased the transition between one and two peaks depending on ensuremath tau 1 and ensuremath lambda is more complex than that depending on ensuremath tau 2

stochastic resonance in a fractional oscillator with random mass and random frequency for a fractional linear oscillator subjected to two multiplicative dichotomous noises and a additive fractional gaussian noise and driven by a periodic signal we study the stochastic resonance sr in this paper using fractional shapiro loginov formula and the laplace transformation technique we acquire the exact expression of the first order moment of the system s steady response meanwhile we discuss the evolutions of the output amplitude with frequency of the periodic signal noise parameters fractional order and friction coefficient we find that sr in the wide sense existing in this system specially the evolution of the output amplitude with frequency of the periodic signal presents one peak oscillation and two peak oscillation moreover the friction coefficient can induce stochastic multi resonance

nonstationary stochastic resonance it is by now established that remarkably the addition of noise to a nonlinear system may sometimes facilitate rather than hamper the detection of weak signals this phenomenon usually referred to as stochastic resonance was originally associated with strictly periodic signals but it was eventually shown to occur for stationary aperiodic signals as well however in several situations of practical interest the signal can be markedly nonstationary we demonstrate that the phenomenon of stochastic resonance extends to nonstationary signals as well and thus could be relevant to a wider class of biological and electronic applications building on both nondynamic and aperiodic stochastic resonance our scheme is based on a multilevel trigger mechanism which could be realized as a parallel network of differentiated threshold sensors we find that optimal detection is reached for a number of thresholds of order 10 and that little is gained by going much beyond that number we raise the question of whether this is related to the fact that evolution has favored some fixed numbers of precisely this order of magnitude in certain aspects of sensory perception

signal to noise ratio gain of a noisy neuron that transmits subthreshold periodic spike trains the transmission properties of an integrate and fire neuron model that transmits coherent subthreshold spike trains in a shot noise environment are investigated by numerical simulation for very weak coherent couplings it is shown that the input output signal to noise ratio snr gain is easier to exceed unity while for stronger coherent couplings it is difficult to observe the snr gain larger than unity at the optimal noise intensity these observations are different from those acquired in the case of continuous noise our analysis further suggests that the larger snr gain in the very weak coherent coupling case should be due to the noise induced resonance it is also shown that there is more possibility of the snr gain above unity for slower periodic spike trains transmitted by the model the results may be useful in understanding the performance of real noisy neurons acting as signal processing elements

harmonic oscillator with multiplicative noise nonmonotonic dependence on the strength and the rate of dichotomous noise the output signal of a undamped linear oscillator with a random frequency subject to a periodic force shows nonmonotonic dependence on the strength and the rate of color noise stochastic resonance the effect is absent for white noise

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

double stochastic resonance in an insect ecosystem with time delays abstract considering additive and multiplicative periodic signals we have investigated the stochastic resonance sr phenomenon in an insect ecosystem with two different types of time delays at which the insect dynamics is assumed to be disturbed by both additive and multiplicative noises the signal to noise ratio snr is calculated when two different weak periodic signals are added to the insect system it is shown from the snr that the additive and multiplicative periodic signals can cause the sr and double sr in the case of time delays in the stochastic and deterministic force respectively a detailed study of the snr depending on various noise characteristics is performed and the main results about sr are compared for two different cases of time delays

shot noise in the leaky integrate and fire neuron we study the influence of noise on the transmission of temporal information by a leaky integrate and fire neuron using the theory of shot noise the model includes a finite number of synapses and has a membrane potential variance de facto modulated by the input signal the phenomenon of stochastic resonance in spiking neurons is analytically exhibited using an inhomogeneous poisson process model of the spike trains and links with the traditional ornstein uhlenbeck process obtained by a diffusion approximation are given it is shown that the modulated membrane potential variance inherent to the model gives better signal processing capabilities than the diffusion approximation

enhancement of stochastic resonance the role of non gaussian noises abstract we have analyzed the phenomenon of stochastic resonance in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation that enables us to get through the two state theory analytical expressions for the signal to noise ratio finding an enhancement of this quantity when the system departs from gaussian behavior this finding is supported by extensive numerical simulations we discuss the relation of these results to some experiments in sensory systems

stochastic multiresonance and correlation time controlled stability for a harmonic oscillator with fluctuating frequency the long time behavior of the first two moments and the correlation function for the output signal of a harmonic oscillator with fluctuating frequency subjected to an external periodic force and an additive thermal noise is considered analytically the colored fluctuations of the oscillator frequency are modeled as a three level markovian noise using the shapiro loginov formula the exact expressions of several stochastic resonance sr characteristics such as the spectral amplification the variance of the output signal the signal to noise ratio and the sr gain have been calculated the nonmonotonic dependence of the sr characteristics versus the noise parameters as well as versus the input signal frequency and also the conditions for the appearance of energetic instability are analyzed in particular the multiresonancelike behavior of the variance and the signal to noise ratio as functions of the noise correlation time are observed and the connection between the occurrence of energetic instability and the phenomenon of stochastic multiresonance is established some unexpected effects such as the hypersensitive response of the spectral amplification to small variations of the noise amplitude encountered in the case of a large flatness of the colored noise are also discussed

comparison of aperiodic stochastic resonance in a bistable system realized by adding noise and by tuning system parameters two methods of realizing aperiodic stochastic resonance asr by adding noise and tuning system parameters in a bistable system after a scale transformation can be compared in a real parameter space in this space the resonance point of asr via adding noise denotes the extremum of a line segment whereas the method of tuning system parameters presents the extrema of a parameter plane we demonstrate that in terms of the system performance the method of tuning system parameters takes the precedence of the approach of adding noise for an adjustable bistable system besides adding noise can be viewed as a specific case of tuning system parameters further research shows that the optimal system found by tuning system parameters may be subthreshold or suprathreshold and the conventional asr effects might not occur in some suprathreshold optimal systems

evaluation of stochastic resonance based detectors of weak harmonic signals in additive white gaussian noise a thorough evaluation of stochastic resonance in the framework of statistical detection theory is presented both as a nonlinear signal preprocessor and as a detector the pertinent receiver operating characteristics are compared with those of the known statistically optimum detector using extensive monte carlo simulations parameter optimization and computational budget aspects are discussed

interference mitigation in spread spectrum communication systems using time frequency distributions the capability of the time frequency distributions tfds to properly represent a single as well as multiple component signals in time and frequency permits the application of a new approach for interference excision in spread spectrum communication systems the instantaneous frequency if estimate from the tfd is used to construct a finite impulse response filter that reduces the interference power with a minimum possible distortion of the desired signal the proposed technique is therefore a case of open loop adaptive filtering three and five coefficient zero phase excision filters are considered closed form expressions of the improvement of snr at the receiver correlator output using the tfd based adaptive filtering are derived for two extreme cases of time varying interferers namely those of fixed frequency sinusoids and randomly changing instantaneous frequencies simulation results including the bit error rates are presented for both swept and frequency hopping jammers

method and apparatus for fundamental frequency extraction or detection in speech an object is to provide a method of extracting sound source information which method enables the characteristics of fixed points of mapping from filter center frequency to output instantaneous frequency to be detected from instantaneous data as a value which can be interpreted quantitatively in a method of extracting sound source information by use of fixed points of mapping from frequency to instantaneous frequency instantaneous frequency of each filter 2 9 is partial differentiated with respect to frequency by an instantaneous frequency frequency differentiation circuit 3 10 to thereby obtain a first value output of each filter is partial differentiated with respect to frequency and then with respect to time by an instantaneous frequency time frequency differentiation circuit 4 11 to thereby obtain a second value and proper weights are imparted to the first and second values and short time weighted integration with respect to time is performed by a carrier to noise ratio calculation circuit 5 12 to estimate a carrier to noise ratio of each filter thus a carrier to noise ratio is obtained and an estimated value of evaluation value is obtained

wave dispersion in periodic post buckled structures wave propagation in pinned supported post buckled beams can be described with the korteweg de vries kdv equation finite element simulations however show that the kdv is applicable only to post buckled beams with strong pre compression for weak and moderate pre stress a dispersive front is present and it is the aim of the current paper to analyze sources of dispersion beyond periodicity given three support types guided pinned and free bloch theorem and a transfer matrix method are employed to obtain numerical dispersion relations and characteristic wave modes which are used to analyze the effects of pre stress initial curvature and the influence of support types additionally a new method is proposed to obtain a semi analytical dispersion equation for the acoustic branch powers of frequency and the propagation constant are explicitly expressed and their coefficients are based on stiffness and mass matrix components obtained from finite elements this allows a physical interpretation of the dispersion sources based on which equivalent mass spring models of post buckled beam are proposed it is found that mass and stiffness coupling are significant dispersion sources in the present paper a reduced form of bloch theorem is presented exploiting glide reflection symmetries reducing the size of the unit cell and allowing an easier representation and interpretation of results

plane wave propagation and frequency band gaps in periodic plates and cylindrical shells with and without heavy fluid loading free plane wave propagation in infinitely long periodic elastic structures with and without heavy fluid loading is considered the structures comprise continuous elements of two different types connected in an alternating sequence in the absence of fluid loading an exact solution which describes wave motion in each unboundedly extended element is obtained analytically as a superposition of all propagating and evanescent waves continuity conditions at the interfaces between elements are formulated and standard floquet theory is applied to set up a characteristic determinant an efficient algorithm to compute bloch parameters propagation constants as a function of the excitation frequency is suggested and the location of band gaps is studied as a function of non dimensional parameters of the structure s composition in the case of heavy fluid loading an infinitely large number of propagating or evanescent waves exist in each unboundedly extended elasto acoustic element of a periodic structure wave motion in each element is then presented in the form of a modal decomposition with a finite number of terms retained in these expansions and the accuracy of such an approximation is assessed a generalized algorithm is used to compute bloch parameters for a periodic structure with heavy fluid loading as a function of the excitation frequency and similarly to the previous case the location of band gaps is studied

theory of stochastic resonance for small signals in weakly damped bistable oscillators the response of a weakly damped bistable oscillator to an external periodic force is considered theoretically in the approximation of weak signals we can write a linearized equation for the signal and the corresponding nonlinear equation for the noise these equations contain two unknown parameters an effective stiffness and an additional damping factor in the case of the weakly damped bistable oscillator considered here the two dimensional fokker planck equation corresponding to the equation for the noise can be solved approximately by changing to a slow variable energy and applying a method of successive approximation this approach allows us to find the unknown parameters and to calculate the amplitude ratio of the output and input signals i e the gain factor

system size stochastic resonance in a model for opinion formation we study a model for opinion formation which incorporates three basic ingredients for the evolution of the opinion held by an individual imitation influence of fashion and randomness we show that in the absence of fashion the model behaves as a bistable system with random jumps between the two stable states with a distribution of times following kramer s law we also demonstrate the existence of system size stochastic resonance by which there is an optimal value for the number of individuals n for which the average opinion follows better the fashion

stochastic resonance with spatiotemporal signal controlled by time delays stochastic resonance in two coupled threshold elements with input periodic signals shifted in phase is studied for fixed phase shift and coupling strength the signal to noise ratio at the output of each element can be maximized by introducing proper time delays in the coupling terms which cancel the effect of the phase shift this shows that in systems of coupled elements driven by spatiotemporal periodic signals stochastic resonance can be controlled by delayed coupling

dynamic response analysis of truss type structural networks a wave propagation approach abstract a typical space structure is composed of piece wise periodic arrays of connected truss units these arrays can intersect each other and form multiple closed loops in this paper a detailed step by step numerical procedure is provided for computing the response of such a structure to external excitations the basic idea is to treat an array of connected truss units as a multi channel waveguide capable of transmitting several types of wave motions each waveguide or each junction where several waveguides intersect can be characterized by a wave scattering matrix which is composed of the transmission and reflection submatrices a reflection submatrix reverses the direction of incoming waves whereas a transmission submatrix permits the incoming waves to enter or to be directed to other waveguides by use of wave scattering matrices in the formulation the numerical computation always follows the directions of propagation of various waves thus numerical stability is assured since the amplitude of wave motion decays as it propagates along a path due to structural damping the numerical procedure described herein represents an extension of the author s previous works by 1 describing for the first time the dynamics of individual truss arrays in terms of scattering matrices 2 adopting a new bookkeeping system to accommodate more complicated configurations of structural networks and 3 developing an efficient procedure to eliminate step by step superfluous unknowns thus simplifying the calculation combination of the three advances makes it possible to treat for the first time such complicated configurations as multiple closed loops since the actual truss type construction is retained when obtaining the wave scattering matrices the procedure is considered more accurate than those based on substitution for truss construction of timoshenko beam elements application of the procedure is illustrated by an example

transport and its enhancement caused by coupling using the weiss mean field approximation theory and the particles transport theory for the spatially periodic stochastic systems we derive an exact analytical expression for the stationary probability current of a coupled lattice system driven by dichotomous noise it is shown that for this coupled lattice system the spatial asymmetry of the system the asymmetry of the dichotomous noise and the coupling among nearest neighbors are the ingredients for the stationary probability current by applying our theory to two special models we find that 1 the coupling can lead to the directional transport of the particles even when the potential and the dichotomous noise are symmetric and 2 the coupling among nearest neighbors can enhance the transport of the particles in some circumstances our results are applied to a device of two dimensional josephson junction arrays and a large protein motors cluster

stochastic resonance in linear system due to dichotomous noise modulated by bias signal the stochastic resonance in an over damped linear system due to dichotomous noise modulated by a bias signal is studied in detail by the theory of signal to noise ratio snr and the shapiro loginov formula the exact expressions of the first two moments and snr for the output to the asymmetric dichotomous noise input are obtained it is found that each curve of the snr versus the multiplicative noise intensity exhibits a mono peak and the conventional stochastic resonance appears which is absent for the case of noise and periodic signal introduced additively meanwhile the snr is a non monotonic function of the signal frequency or the correlation time of noise and the bona fide stochastic resonance sr and sr in a broad sense exist moreover the snr depends on the additive noise intensity cross correlation strength and asymmetry of multiplicative noise

propagation of decaying waves in periodic and piecewise periodic structures of finite length abstract a new method is described for the analysis of long and complicated structures which are composed of spatially periodic units or sections of spatially periodic units the response of such a structure to external excitations is treated as a superposition of wave motions with account taken of the effects of wave reflection due to change in the construction pattern along the structure and boundary conditions since damping usually exists in a real structure a wave motion always decays as it propagates along the structure however this can cause numerical difficulties if the structure is rather long because a decaying wave appears as a growing wave in the opposite direction and since propagations in both directions must be accounted for in the analysis computational errors associated with the apparent growing waves also grow and the numerical results become meaningless in the proposed new scheme use is made of wave reflection and transmission matrices making it possible for all computations to proceed in the direction of wave propagation so that the results are always stable numerically furthermore the required computing time is greatly reduced in comparison with that of an all encompassing finite element analysis for the entire structure application of the new method is illustrated by examples

aperiodic stochastic resonance stochastic resonance sr is a phenomenon wherein the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular level of noise recently we presented a method and theory for characterizing sr type behavior in excitable systems with aperiodic i e broadband input signals phys rev e 52 r3321 1995 we coined the term aperiodic stochastic resonance asr to describe this general type of behavior in that earlier study we demonstrated asr in the fitzhugh nagumo neuronal model here we demonstrate asr in three additional systems a bistable well system an integrate and fire neuronal model and the hodgkin huxley hh neuronal model we present computational and theoretical results for each system in the context of the hh model we develop a general theory for asr in excitable membranes this work clearly shows that sr type behavior is not limited to systems with periodic inputs thus in general noise can serve to enhance the response of a nonlinear system to a weak input signal regardless of whether the signal is periodic or aperiodic textcopyright 1996 the american physical society

stochastic resonance in a periodically driven linear system with multiplicative and periodically modulated additive white noises abstract the stochastic resonance sr of periodically driven linear system with multiplicative white noise and periodically modulated additive white noise is studied exact expressions of output signal to noise ratio are obtained the sr characteristics features are shown in two different situations the driven frequency is equal to the modulative frequency 1 and the driven frequency is not equal to the modulative frequency 1 the result was as follows the exact expression of output signal to noise ratio snr exhibits sr in three aspects in the case of 1 1 the curve of snr versus noise strength q exists a resonance peak this is a standard form of sr 2 a resonance peak exists in the snr vs curve in the region of 0 3 a maximum appears in the curve of snr as a function of the characteristic of signal itself the signal frequency it is of interest to examine the snr in the case of 1 from the exact expression of snr we see for 1 that the snr vs q curve exhibits a minimum firstly then a maximum that is to say it exhibits a suppression firstly resonance later and is very different from the case of 1