a direct approach to the exit problem this paper considers the problem of exit for a dynamical system driven by small white noise from the domain of attraction of a stable state a direct singular perturbation analysis of the forward equation is presented based on kramers approach in which the solution to the stationary fokker planck equation is constructed for a process with absorption at the boundary and a source at the attractor in this formulation the boundary and matching conditions fully determine the uniform expansion of the solution without resorting to external selection criteria for the expansion coefficients such as variational principles or the lagrange identity as in our previous theory the exit density and the mean first passage time to the boundary are calculated from the solution of the stationary fokker planck equation as the probability current density and as the inverse of the total flux on the boundary respectively as an application a uniform expansion is constructed for the escape rate in kramers problem o

a finite element spectral method for approximating the time harmonic maxwell system in r 3 we describe and analyze a method for computing an approximation to the time harmonic electromagnetic field scattered by a bounded inhomogeneity the method is to couple a finite element scheme on a bounded domain with a series solution outside the bounded domain the main result of the paper is to show that the proposed numerical scheme possesses a unique solution with quasi optimal approximation properties we do this by verifying the conditions of the babuska brezzi theory for saddle point problems in analyzing the continuous problem we also provide a new variational proof of the existence of solutions of the continuous maxwell problem

sensitivity analysis of the stochastically and periodically forced brusselator abstract the problem of sensitivity of nonlinear system limit cycle with respect to small stochastic and periodic disturbances is considered sensitivity analysis on the basis of quasipotential function is performed the quasipotential is used widely in statistical physics for instance by graham for analysis of nonequilibrium thermodynamics problem we consider an application of quasipotential technique to sensitivity problem for the plane orbit case an approximation of quasipotential is expressed by some scalar function this function sensitivity function is introduced as a base tool of a quantitative description for a system response on the external disturbances new cycle characteristics sensitivity factor parameter of stiffness are considered the analysis of the forced brusselator based on sensitivity function is shown from this analysis the critical value of brusselator parameter is found the dynamics of forced brusselator for this critical value is investigated for small stochastic disturbances the burst of response amplitude is shown for small periodic disturbances the period doubling regime of the transition to chaos scenario is demonstrated

analysis of a finite element method for maxwell s equations the use of finite elements to discretize the time dependent maxwell equations on a bounded domain in three dimensional space is analyzed energy norm error estimates are provided when general finite element methods are used to discretize the equations in space in addition it is shown that if some curl conforming elements due to nedelec are used error estimates may also be proved in the l 2 norm

an analysis of new and existing fdtd methods for isotropic cold plasma and a method for improving their accuracy over the past few years a number of different finite difference time domain fdtd methods for modeling electromagnetic propagation in an isotropic cold plasma have been published we have analyzed the accuracy and stability of these methods to determine which method provides the greatest accuracy for a given computation time for completeness two new fdtd methods for cold plasma one of which is based on the concept of exponential fitting are introduced and evaluated along with the existing methods we also introduce the concept of cutoff modification which can be easily applied to most of the fdtd methods and which we show can improve the accuracy of these methods with no additional computational cost von neumann s stability analysis is used to evaluate the stability of the various methods and their accuracy is determined from a straightforward time and space harmonic analysis of the dispersion and dissipation errors results of numerical experiments to verify the accuracy analysis are presented it is found that for low loss plasma the piecewise linear recursive convolution method plrc method is the most accurate but the method of young see radio sci vol 29 p 1513 22 1994 can use less memory and is nearly as accurate in this low loss plasma regime cutoff modification can significantly reduce the error near cutoff at the expense of slightly greater error at lower frequencies for strongly collisional plasmas the plrc method also provides the most accurate solution

global threshold dynamics of a stochastic differential equation sis model abstract in this paper we further investigate the global dynamics of a stochastic differential equation sis susceptible infected susceptible epidemic model recently proposed in gray et al 2011 8 we present a stochastic threshold theorem in term of a stochastic basic reproduction number r 0 s the disease dies out with probability one if r 0 s 1 and the disease is recurrent if r 0 s 1 we prove the existence and global asymptotic stability of a unique invariant density for the fokker planck equation associated with the sde sis model when r 0 s 1 in term of the profile of the invariant density we define a persistence basic reproduction number r 0 p and give a persistence threshold theorem the disease dies out with large probability if r 0 p 1 while persists with large probability if r 0 p 1 comparing the stochastic disease prevalence with the deterministic disease prevalence we discover that the stochastic prevalence is bigger than the deterministic prevalence if the deterministic basic reproduction number r 0 d 2 this shows that noise may increase severity of disease finally we study the asymptotic dynamics of the stochastic sis model as the noise vanishes and establish a sharp connection with the threshold dynamics of the deterministic sis model in term of a limit stochastic threshold theorem

quasiperiodically driven maps in the low dissipation limit received 24 september 2012 revised manuscript received 18 february 2013 published 11 march 2013 we study the quasiperiodically driven henon and standard maps in the weak dissipative limit in the absence of forcing there are a large number of coexisting periodic attractors although chaotic attractors can also be found these typically have vanishingly small basins of attraction quasiperiodic forcing reduces the multistability in thesystem and as the bifurcation parameter is varied strange nonchaotic attractors snas are created the attractorbasin for snas appears to be the largest among those of all coexisting attractors at such a transition doi 10 1103 physreve 87 034901 pacs number s 05

noisy fitzhugh nagumo model from single elements to globally coupled networks we study the noisy fitzhugh nagumo model representative of the dynamics of excitable neural elements and derive a fokker planck equation for both a single element and for a network of globally coupled elements we introduce an efficient way to numerically solve this fokker planck equation especially for large noise levels we show that contrary to the single element the network can undergo a hopf bifurcation as the coupling strength is increased furthermore we show that an external sinusoidal driving force leads to a classical resonance when its frequency matches the underlying system frequency this resonance is also investigated analytically by exploiting the different time scales in the problem

discreteness induced stochastic steady state in reaction diffusion systems self consistent analysis and stochastic simulations abstract a self consistent equation to derive a discreteness induced stochastic steady state is presented for reaction diffusion systems for this formalism we use the so called kuramoto length a typical distance over which a molecule diffuses in its lifetime as was originally introduced to determine if local fluctuations influence globally the whole system we show that this kuramoto length is also relevant to determine whether the discreteness of molecules is significant or not if the number of molecules of a certain species within the kuramoto length is small and discrete localization of some other chemicals is brought about which can accelerate certain reactions when this acceleration influences the concentration of the original molecule species it is shown that a novel stochastic steady state is induced that does not appear in the continuum limit a theory to obtain and characterize this state is introduced based on the self consistent equation for chemical concentrations this stochastic steady state is confirmed by numerical simulations on a certain reaction model which agrees well with the theoretical estimation formation and coexistence of domains with different stochastic states are also reported which is maintained by the discreteness relevance of our result to intracellular reactions is briefly discussed

solution of the boundary value problem for optimal escape in continuous stochastic systems and maps topologies of invariant manifolds and optimal trajectories are investigated in stochastic continuous systems and maps a topological method is introduced that simplifies the solution of boundary value problems the activation energy is calculated as a function of a set of parameters characterizing the initial conditions of the escape path the method is applied explicitly to compute the optimal escape path and the activation energy for a variety of dynamical systems and maps

multistability noise and attractor hopping the crucial role of chaotic saddles we investigate the hopping dynamics between different attractors in a multistable system under the influence of noise using symbolic dynamics we find a sudden increase of dynamical entropies when a system parameter is varied this effect is explained by a bifurcation involving two chaotic saddles we also demonstrate that the transient lifetimes on the saddle obey a scaling law in analogy to crisis

sudden change from chaos to oscillation death in the bonhoeffer van der pol oscillator under weak periodic perturbation in this paper we analyze the sudden change from chaos to oscillation death generated by the bonhoeffer van der pol bvp oscillator under weak periodic perturbation the parameter values of the bvp oscillator are chosen such that a stable focus and a stable relaxation oscillation coexist if no perturbation is applied in such a system complicated bifurcation structure is expected to emerge when weak periodic perturbation is applied because the stable focus and the stable relaxation oscillation coexist in close proximity in the phase plane we draw a bifurcation diagram of the fundamental harmonic entrainment the bifurcation structure is complex because there coexist two bifurcation sets one is the bifurcation set generated in the vicinity of the stable focus and the other is that generated in the vicinity of the stable relaxation oscillation by analyzing the bifurcation diagram in detail we can explain the sudden change from chaos with complicated waveforms to oscillation death we make it clear that this phenomenon is caused by a saddle node bifurcation

noise in unspecified non linear time series abstract in this paper a method is developed which allows the determination of the noise level the size of external shocks which is present in a linear or non linear autoregressive time series nothing need to be known about the functional form or about the lag structure of the underlying model the technique regards the time series as a hypersurface lying in a higher dimensional embedding space and makes use of the correlation integral as introduced in the physical sciences uniformly distributed noise is considered at first then the technique is generalized to normal and other distributions and even if the distribution of the noise is unknown one can still make comparisons between the intensities of noise in different time series the method is put to a test with empirically assessed stock market data

global superconvergence for maxwell s equations in this paper the global superconvergence is analysed on two schemes a mixed finite element scheme and a finite element scheme for maxwell s equations in r 3 such a supercovergence analysis is achieved by means of the technique of integral identity which has been used in the supercovergence analysis for many other equations and schemes on a rectangular mesh and then are generalized into more general domains and problems with the variable coefficients besides being more direct our analysis generalizes the results of monk

stochastic sensitivity of the closed invariant curves for discrete time systems abstract discrete time nonlinear systems with invariant closed smooth curves forced by random disturbances are studied constructive approximations of the corresponding probabilistic distributions near these curves based on stochastic sensitivity functions are suggested for stochastic sensitivity matrix functions the linear equations are obtained for descriptive visualization of this technique a method of confidence domains is used the elaborated theory is illustrated on the example of the two dimensional model

stochastic sensitivity analysis of noise induced intermittency and transition to chaos in one dimensional discrete time systems abstract we study a phenomenon of noise induced intermittency for the stochastically forced one dimensional discrete time system near tangent bifurcation in a subcritical zone where the deterministic system has a single stable equilibrium even small noises generate large amplitude chaotic oscillations and intermittency we show that this phenomenon can be explained by a high stochastic sensitivity of this equilibrium for the analysis of this system we suggest a constructive method based on stochastic sensitivity functions and confidence intervals technique an explicit formula for the value of the noise intensity threshold corresponding to the onset of noise induced intermittency is found on the basis of our approach a parametrical diagram of different stochastic regimes of intermittency and asymptotics are given

singularities of fluctuational paths for an overdamped two well system driven by white noise abstract noise induced escape from a metastable state in an overdamped double well system is investigated with the wkb approximation employed the pattern of fluctuational paths is given by using the action plot which gives rise to mpeps the pattern is divided into various regions where fluctuational paths inside show qualitatively distinguished characteristics the global quasi potential is calculated and its value at the saddle on the boundary agrees with the one obtained by action plot we show a contour and 3d plot of the quasi potential to illustrate the relative stabilities of metastable states the bifurcations of singularities as the system parameter varies are analyzed by the second order term of the wkb expansion in the vicinity of x axis its asymptotic behavior determines the positions of cusps and furthermore its evolution turns out to delineate the twisting structure of the lagrangian manifold

phase locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies abstract we study phase locking in a network of coupled nonlinear oscillators with local interactions and random intrinsic frequencies the oscillators are located at the vertices of a graph and interact along the edges they are coupled by sinusoidal functions of the phase differences across the edges and their intrinsic frequencies are independent and identically distributed with finite mean and variance we derive an exact expression for the probability of phase locking in a linear chain of such oscillators and prove that this probability tends to zero as the number of oscillators grows without bound however if the coupling strength increases as the square root of the number of oscillators the probability of phase locking tends to a limiting distribution the kolmogorov smirnov distribution this latter result is obtained by showing that the phase locking problem is equivalent to a discretization of pinned brownian motion the results on chains of oscillators are extended to more general graphs in particular for a hypercubic lattice of any dimension the probability of phase locking tends to zero exponentially fast as the number of oscillators grows without bound we also consider a less stringent type of synchronization characterized by large clusters of oscillators mutually entrained at the same average frequency it is shown that if such clusters exist they necessarily have a sponge like geometry

superconvergence analysis for maxwell s equations in dispersive media in this paper we consider the time dependent maxwell s equations in dispersive media on a bounded three dimensional domain global superconvergence is obtained for semi discrete mixed finite element methods for three most popular dispersive media models the isotropic cold plasma the one pole debye medium and the two pole lorentz medium global superconvergence for a standard finite element method is also presented to our best knowledge this is the first superconvergence analysis obtained for maxwell s equations when dispersive media are involved

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

the influence of noise on the logistic model the behavior of the logistic system which is generated by the functionf x ax 1 x changes in an interesting way if it is perturbed by external noise it turns out that the chaotic behavior which was predicted by li and yorke for orbits of period 3 becomes visible and that a sequence of mergence transitions occurs at the critical parameter the change of the invariant probability density and the lyapunov exponents are examined numerically the power spectrum for the period 3 orbit for different fluctuations is calculated and a recursion formula for the time evolution of the probability density is presented as a discrete time analog of a chapman kolmogorov equation

crossing the quasi threshold manifold of a noise driven excitable system we consider the noise induced escapes in an excitable system possessing a quasi threshold manifold along which there exists a certain point of minimal quasi potential in the weak noise limit the optimal escaping path turns out to approach this particular point asymptotically making it analogous to an ordinary saddle numerical simulations are performed and an elaboration on the effect of small but finite noise is given which shows that the ridges where the prehistory probability distribution peaks are located mainly within the region where the quasi potential increases gently the cases allowing anisotropic noise are discussed and we found that varying the noise term in the slow variable would dramatically raise the whole level of quasi potentials leading to significant changes in both patterns of optimal paths and exit locations

constructive analysis of noise induced transitions for coexisting periodic attractors of the lorenz model we study the stochastically forced lorenz model in the parameter zone admitting two coexisting limit cycles under the transition to chaos via period doubling bifurcations noise induced transitions between both different parts of the single attractor and two coexisting separate attractors are demonstrated the effects of structural stabilization and noise symmetrization are discussed we suggest a stochastic sensitivity function technique for the analysis of noise induced transitions between two coexisting limit cycles this approach allows us to construct the dispersion ellipses of random trajectories for any poincare sections possibilities of our descriptive geometric method for a detailed analysis of noise induced transitions between two periodic attractors of lorenz model are demonstrated

critical dynamics of the bonhoeffer van der pol equation and its chaotic response to periodic stimulation abstract we consider the bonhoeffer van der pol equation as a prototype model for excitable systems for this equation we investigate the effect of application of a periodic stimulus in a critical range of values for stimulus strength and period we find depending on the choice of those values many different response types which include quasi periodic and chaotic behavior we present phase portraits and bifurcation diagrams to illustrate these responses the study of an associated local equation shows that the same types of behavior may be expected in a whole class of related equations we discuss the relevance of our results for a number of biological and physiological applications

stochastic bifurcation in fitzhugh nagumo ensembles subjected to additive and or multiplicative noises abstract we have studied the dynamical properties of finite n unit fitzhugh nagumo fn ensembles subjected to additive and or multiplicative noises reformulating the augmented moment method amm with the fokker planck equation fpe method h hasegawa j phys soc japan 75 2006 033001 in the amm original 2 n dimensional stochastic equations are transformed to eight dimensional deterministic ones and the dynamics is described in terms of averages and fluctuations of local and global variables the stochastic bifurcation is discussed by a linear stability analysis of the deterministic amm equations the bifurcation transition diagram of multiplicative noise is rather different from that of additive noise the former has the wider oscillating region than the latter the synchronization in globally coupled fn ensembles is also investigated results of the amm are in good agreement with those of direct simulations dss

topological features of large fluctuations to the interior of a limit cycle received 29 october 1996 we investigate the pattern of optimal paths along which a dynamical system driven by weak noise moves with overwhelming probability when it fluctuates far away from a stable state our emphasis is on systems that perform self sustained periodic vibrations and have an unstable focus inside a stable limit cycle we show that in the vicinity of the unstable focus the flow field of optimal paths generically displays a pattern of singularities in particular it contains a switching line that separates areas to which the system arrives along optimal paths of topologically different types the switching line spirals into the focus and has a self similar structure depending on the behavior of the system near the focus it may be smooth or have finite length branches our results are based on an analysis of the topology of the lagrangian manifold for an auxiliary purely dynamical problem that determines the optimal paths we illustrate our theory by studying both theoretically and numerically a van der pol oscillator driven by weak white noise s1063 651x 97 02703 7 many nonlinear dissipative systems display stable periodic oscillations i e their state spaces contain stable limit cycles 1 examples include lasers 2 radiofrequency generators 1 a chemical 3 a and biological 3 b systems in many cases the vibrations are nonsinusoidal as in a multimode laser with strong mode coupling 4 passive optically bistable elements 5 and various sorts of engineering structure 6 fluctuations in periodically oscillating systems play an extremely important role they eventually destroy periodicity of the self sustained oscillations so that the oscillation phase becomes random and a stationary probability distribution in the state space of the system is formed 7 8 this distribution reaches a maximum at the cycle does not vary much along the cycle and falls off rapidly in directions transverse to the cycle the shape of the maximum depends on the character of small transverse fluctuations away from the cycle if the fluctuations are due to the system being perturbed by weak noise of intensity d the transverse falloff will usually be approximately gaussian 7 9 with standard deviation proportional to d 1 2 as d 0

glottal volume velocity waveform characteristics in subjects with and without vocal training related to gender sound intensity fundamental frequency and age glottal volume velocity waveform characteristics of 224 subjects categorized in four groups according to gender and vocal training were determined and their relations to sound pressure level fundamental frequency intra oral pressure and age were analyzed subjects phonated at three intensity conditions the glottal volume velocity waveforms were obtained by inverse filtering the oral flow glottal volume velocity waveforms were parameterized with flow based minimum flow ac flow average flow maximum flow declination rate and time based parameters closed quotient closing quotient speed quotient as well as with derived parameters vocal efficiency and glottal resistance higher sound pressure levels intra oral pressures and flow parameter values ac flow maximum flow declination rate were observed when compared with previous investigations these higher values might be the result of the specific phonation tasks stressed ae vowel in a word and a sentence or filtering processes few statistically significant p 0 01 differences in parameters were found between untrained and trained subjects the maximum flow declination rate and the closing quotient were higher in trained women p 0 001 and the speed quotient was higher in trained men p 0 005 several statistically significant parameter differences were found between men and women minimum flow ac flow average flow maximum flow declination rate closing quotient glottal resistance p 0 001 and closed quotient p 0 005 significant effects of intensity condition were observed on ac flow maximum flow declination rate closing quotient and vocal efficiency in women p 0 005 and on minimum flow ac flow average flow maximum flow declination rate closed quotient and vocal efficiency in men p 0 01

escape from attracting sets in randomly perturbed systems the dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science previous studies of escape in chaotic systems have rather focused on the case of unbounded noise usually assumed to have gaussian distribution in this paper we address the problem of escape induced by bounded noise we show that the dynamics of escape from an attractor s basin is equivalent to that of a closed system with an appropriately chosen hole using this equivalence we show that there is a minimum noise amplitude above which escape takes place and we derive analytical expressions for the scaling of the escape rate with noise amplitude near the escape transition we verify our analytical predictions through numerical simulations of two well known two dimensional maps with noise

an amplitude quotient based method to analyze changes in the shape of the glottal pulse in the regulation of vocal intensity this study presents an approach to visualizing intensity regulation in speech the method expresses a voice sample in a two dimensional space using amplitude domain values extracted from the glottal flow estimated by inverse filtering the two dimensional presentation is obtained by expressing a time domain measure of the glottal pulse the amplitude quotient aq as a function of the negative peak amplitude of the flow derivative dpeak the regulation of vocal intensity was analyzed with the proposed method from voices varying from extremely soft to very loud with a spl range of approximately 55db when vocal intensity was increased the speech samples first showed a rapidly decreasing trend as expressed on the proposed aq dpeak graph when intensity was further raised the location of the samples converged toward a horizontal line the asymptote of a hypothetical hyperbola this behavior of the aq dpeak graph indicates that the intensity regulation strategy changes from laryngeal to respiratory mecha

stochastic transient of a noisy van der pol oscillator abstract transient characteristics of a van der pol oscillator perturbed by additive and multiplicative noises of different non linearities are studied and compared systematically we numerically determine the noise dependence of the period and of the life time of a noisy oscillator attraction basins and stability are also investigated for the trivial fixed point and the limit cycle

noise induced order ii a curious noise effect in certain maps reported earlier is investigated further a striking feature of these maps is obtained in the symbolic dynamical approach the decrease of entropy is attributed to a simple mechanism which deletes certain states in the symbolic dynamics and the value of the modified entropy is calculated based on this picture

computation of true chaotic orbits using cubic irrationals abstract we introduce a method that enables us to generate long true orbits of discrete time dynamical systems defined by one dimensional piecewise linear fractional maps with integer coefficients the method uses cubic irrationals to represent numbers and involves only integer arithmetic to compute true orbits by applying the method to the bernoulli map and a modified bernoulli map we show that it successfully generates true chaotic and intermittent orbits respectively in contrast with conventional simulation methods we demonstrate through simulations concerning invariant measures and the power spectrum that the statistical properties of the true orbits generated agree well with those of typical orbits of the two maps

time domain matched interface and boundary mib modeling of debye dispersive media with curved interfaces a new finite difference time domain fdtd method is introduced for solving transverse magnetic maxwell s equations in debye dispersive media with complex interfaces and discontinuous wave solutions based on the auxiliary differential equation approach a hybrid maxwell debye system is constructed which couples the wave equation for the electric component with maxwell s equations for the magnetic components this hybrid formulation enables the calculation of the time dependent parts of the interface jump conditions so that one can track the transient changes in the regularities of the electromagnetic fields across a dispersive interface effective matched interface and boundary mib treatments are proposed to rigorously impose the physical jump conditions which are not only time dependent but also couple both cartesian directions and both magnetic field components based on a staggered yee lattice the proposed mib scheme can deal with arbitrarily curved interfaces and nonsmooth interfaces with sharped edges second order convergences are numerically achieved in solving dispersive interface problems with constant curvatures general curvatures and nonsmooth corners

dynamics of a limit cycle oscillator under time delayed linear and nonlinear feedbacks abstract we study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single hopf bifurcation oscillator our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips frequency suppression multiple periodic states and chaos such phenomena are frequently observed in the collective behavior of a large number of coupled limit cycle oscillators our time delayed feedback model offers a simple paradigm for obtaining and investigating these temporal states in a single oscillator we construct a detailed bifurcation diagram of the oscillator as a function of the time delay parameter and the driving strengths of the feedback terms we find some new states in the presence of the quadratic nonlinear feedback term with interesting characteristics like birhythmicity phase reversals radial trapping phase jumps and spiraling patterns in the amplitude space our results may find useful applications in physical chemical or biological systems

convergence and superconvergence of a fully discrete scheme for multi term time fractional diffusion equations using finite element method in spatial direction and classical l1 approximation in temporal direction a fully discrete scheme is established for a class of two dimensional multi term time fractional diffusion equations with caputo fractional derivatives the stability analysis of the approximate scheme is proposed the spatial global superconvergence and temporal convergence of order o h2 2 for the original variable in h1 norm is presented by means of properties of bilinear element and interpolation postprocessing technique where h and are the step sizes in space and time respectively finally several numerical examples are implemented to evaluate the efficiency of the theoretical results

identifying stochastic basin hopping by partitioning with graph modularity abstract it has been known that noise in a stochastically perturbed dynamical system can destroy what was the original zero noise case barriers in the phase space pseudobarrier noise can cause the basin hopping we use the frobenius perron operator and its finite rank approximation by the ulam galerkin method to study transport mechanism of a noisy map in order to identify the regions of high transport activity in the phase space and to determine flux across the pseudobarriers we adapt a new graph theoretical method which was developed to detect active pseudobarriers in the original phase space of the stochastic dynamic previous methods to identify basins and basin barriers require a priori knowledge of a mathematical model of the system and hence cannot be applied to observed time series data of which a mathematical model is not known here we describe a novel graph method based on optimization of the modularity measure of a network and introduce its application for determining pseudobarriers in the phase space of a multi stable system only known through observed data

use of hamiltonian mechanics in systems driven by colored noise the evaluation of the path integral representation for stochastic processes in the weak noise limit shows that these systems are governed by a set of equations which are those of a classical dynamics we show that even when the noise is colored these may be put into a hamiltonian form which leads to better insights and improved numerical treatments we concentrate on solving hamilton s equations over an infinite time interval in order to determine the leading order contribution to the mean escape time for a bistable potential the paths may be oscillatory and inherently unstable in which case one must use a multiple shooting numerical technique over a truncated time period in order to calculate the infinite time optimal paths to a given accuracy we look at two systems in some detail the underdamped langevin equation driven by external exponentially correlated noise and the overdamped langevin equation driven by external quasi monochromatic noise we deduce that caustics focusing and bifurcation of the optimal path are general features of all but the simplest stochastic processes

entropy of random chaotic interval map with noise which causes coarse graining abstract a random chaotic interval map with noise which causes coarse graining induces a finite state markov chain for a map topologically conjugate to a piecewise linear map with the lebesgue measure being ergodic we prove that the shannon entropy for the induced markov chain possesses a finite limit as the noise level tends to zero in most cases the limit turns out to be strictly greater than the lyapunov exponent of the original map without noise

anisotropic linear triangle finite element approximation for multi term time fractional mixed diffusion and diffusion wave equations with variable coefficient on 2d bounded domain abstract a fully discrete approximate scheme is established for the 2d multi term time fractional mixed diffusion and diffusion wave equations with spatial variable coefficient by using linear triangle finite element method in space and classical l 1 time stepping method combined with crank nicolson scheme in time then the unconditionally stable analysis of the fully discrete scheme is presented by employing some important lemmas at the same time both the spatial superclose property in h 1 norm and convergence result in l 2 norm are derived by skillfully dealing with numerical errors without any restrictions of time step and mesh size h as a necessary way for obtaining the aimed numerical analysis the relationship between the nonstandard projection operator r h and the interpolation operator i h of linear triangle finite element is introduced moreover the global superconvergence is deduced by adopting interpolation postprocessing technique finally numerical tests are provided to illustrate the efficiency and correctness of the theoretical results

stationary probability distribution near stable limit cycles far from hopf bifurcation points we obtain analytic results for the stationary probability distribution in the vicinity of a stable limit cycle for markov systems described by a fokker planck equation or a birth death master equation the results apply best for ranges of parameters removed from hopf bifurcation points as a by product we demonstrate that there holds a liouville like theorem for the stationary probability distribution the product of the velocity along the limit cycle times the area of the cross section of the probability distribution transverse to the cycle is a constant a numerical simulation of a chemical model system with a limit cycle shows good agreement with the analytic results

quasipotential approach to critical scaling in noise induced chaos when a dynamical system exhibits transient chaos and a nonchaotic attractor as in a periodic window noise can induce a chaotic attractor in particular when the noise amplitude exceeds a critical value the largest lyapunov exponent of the attractor of the system starts to increase from zero while a scaling law for the variation of the lyapunov exponent with noise was uncovered previously it is mostly based on numerical evidence and a heuristic analysis this paper presents a more general approach to the scaling law one based on the concept of quasipotentials besides providing deeper insights into the problem of noise induced chaos the quasipotential approach enables previously unresolved issues to be addressed the fractal properties of noise induced chaotic attractors and applications to biological systems are also discussed

initial validation of an indirect measure of subglottal pressure during vowels some methods for direct measurement of subglottal pressure during speech are invasive and thus cannot be used on a routine basis the development of noninvasive techniques is thus desirable and a simple indirect method for measuring subglottal pressure from records of oral pressure during consonants has recently been proposed and applied to studies of glottal resistance during phonation in order to be useful indirect measurement procedures should be validated by comparisons with direct measurements and the present experiment was designed for such a comparison miniature pressure transducers were used to obtain records of pressure below and above the glottis results showed nonsignificant differences and a high correlation between the direct and indirect measurements this indirect method for measuring subglottal pressure thus appears to provide valid results

analysis of a time domain finite element method for 3 d maxwell s equations in dispersive media abstract we consider the time dependent maxwell s equations in dispersive media on a bounded domain in three dimensional space a fully discrete finite element scheme is developed to approximate the electric field equation derived from the maxwell s equations optimal energy norm error estimates are proved for nedelec curl conforming edge elements this is the first finite element error analysis for maxwell s equations in dispersive media

method of stochastic sensitivity synthesis in a stabilisation problem for nonlinear discrete systems with incomplete information abstracta problem of the synthesis of the assigned probabilistic distribution near the equilibrium of stochastic nonlinear discrete time system with incomplete state information is considered we construct a static feedback regulator which provides a required stochastic sensitivity of this equilibrium it is shown that this problem is reduced to the solution of some quadratic matrix equations the solvability of these quadratic equations is analysed and attainability sets are described in the two dimensional case two variants of the control input are discussed and compared these general results are applied to the suppression of large amplitude oscillations around the equilibria of the stochastically forced henon model with noisy observations we show how suggested control technique by minimising the stochastic sensitivity allows us to suppress chaos and provide a structural stabilisation

superconvergence analysis of nonconforming mixed finite element methods for time dependent maxwell s equations in isotropic cold plasma media in this paper based on our previous work of asymptotic expansion an initial effort of global superconvergence analysis of time domain maxwell s equations in isotropic cold plasma media is obtained for semi discrete mixed finite element scheme during this procedure superclose analysis of the interpolation of the smoothing solution and the solution of mixed finite element method is obtained for the first time by the post processing operators superconvergence phenomena can be found to our best knowledge this is the first global superconvergence analysis presented by nonconforming mixed finite element methods when isotropic cold plasma media is involved

noise induced critical behavior in a multistable system abstract we consider an rf squid coupled to an external magnetic flux consisting of dc and random gaussian distributed components the response of the device to this flux is analysed in the presence of weak multiplicative fluctuations that manifest themselves in the form of a fluctuating nonlinearity parameter it is seen that the presence of this multiplicative noise leads to new critical behavior and the onset of hysteresis phenomena even when the system parameters assume their sub threshold values the effects of varying the relative magnitudes of the additive and multiplicative noise variances are analysed through an evaluation of the probability density function of the total flux in the squid ring

stochastic operators information and entropy for a stochastic operatoru on andl1 space i eu is linear positive and norm preserving on the positive cone ofl1 it is shown thatu decreases relative information between two nonnegativel1 functions furthermore it is shown that the following properties ofu are closely related u is energy decreasing energy preserving u ish decreasing whereh is boltzmann sh functional and the maxwell distributions are fixed points ofu

stochastic analysis of a hopf bifurcation master equation approach the effect of inhomogeneous fluctuations in a reaction diffusion system exhibiting a hopf bifurcation is analyzed using the master equation approach a taylor expansion of the logarithm of the stationary probability known as the stochastic potential is calculated this procedure displays marked analogies with the theory of normal forms the critical potential reduced to its local expansion around an arbitrary point of the limit cycle brings out the essential role played by the phase of the oscillating variables a comparison with the langevin analysis of walgraefet al j chem phys 78 6 3043 1983 is performed

cooperation principle stability and bifurcation in random complex dynamics abstract we investigate the random dynamics of rational maps and the dynamics of semigroups of rational maps on the riemann sphere c we show that regarding random complex dynamics of polynomials generically the chaos of the averaged system disappears at any point in c due to the automatic cooperation of the generators we investigate the iteration and spectral properties of transition operators acting on the space of holder continuous functions on c we also investigate the stability and bifurcation of random complex dynamics we show that the set of stable systems is open and dense in the space of random dynamical systems of polynomials moreover we prove that for a stable system there exist only finitely many minimal sets each minimal set is attracting and the orbit of a holder continuous function on c under the transition operator tends exponentially fast to the finite dimensional space u of finite linear combinations of unitary eigenvectors of the transition operator combining this with the perturbation theory for linear operators we obtain that for a stable system constructed by a finite family of rational maps the projection to the space u depends real analytically on the probability parameters by taking a partial derivative of the function of probability of tending to a minimal set with respect to a probability parameter we introduce a complex analogue of the takagi function which is a new concept

escape problem for irreversible systems the problem of noise induced escape from a metastable state arises in physics chemistry biology systems engineering and other areas the problem is well understood when the underlying dynamics of the system obey detailed balance when this assumption fails many of the results of classical transition rate theory no longer apply and no general method exists for computing the weak noise asymptotic behavior of fundamental quantities such as the mean escape time in this paper we present a general technique for analyzing the weak noise limit of a wide range of stochastically perturbed continuous time nonlinear dynamical systems we simplify the original problem which involves solving a partial differential equation into one in which only ordinary differential equations need be solved this allows us to resolve some old issues for the case when detailed balance holds when it does not hold we show how the formula for the asymptotic behavior of the mean escape time depends on the dynamics of the system along the most probable escape path we also present results on short time behavior and discuss the possibility of ital focusing along the escape path

noise induced global asymptotic stability we prove analytically that additive and parametric multiplicative gaussian distributed white noise interpreted in either the it6 or stratonovich formalism induces global asymptotic stability in two prototypical dynamical systems designated as supercritical the landau equation and subcritical respectively in both systems without noise variation of a parameter leads to a switching between a single globally stable steady state and multiple locally stable steady states with additive noise this switching is mirrored in the behavior of the extrema of probability densities at the same value of the parameter however parametric noise causes a noise amplitude dependent shift postponement in the parameter value at which the switching occurs it is shown analytically that the density converges to a dirac delta function when the solution of the fokker planck equation is no longer normalizable

stochastic sensitivity analysis of noise induced order chaos transitions in discrete time systems with tangent and crisis bifurcations abstract we study noise induced order chaos transitions in discrete time systems with tangent and crisis bifurcations to study these transitions parametrically we suggest a generalized mathematical technique using stochastic sensitivity functions and confidence domains for randomly forced equilibria cycles and chaotic attractors this technique is demonstrated in detail for the simple one dimensional stochastic system in which points of crisis and tangent bifurcations are borders of the order window lying between two chaotic parametric zones a stochastic phenomenon of the extension and shift of this window towards crisis bifurcation point under increasing noise is presented and analyzed shifts of borders of this order window are found as functions of the noise intensity by our analytical approach based on stochastic sensitivity functions we construct a parametric diagram of chaotic and regular regimes for the stochastically forced system

a posteriori error indicators for maxwell s equations abstract in this paper we shall analyze a class of a posteriori error indicators for an electromagnetic scattering problem for maxwell s equations in the presence of a bounded inhomogeneous and anisotropic scatterer problems of this type arise when computing the interaction of electromagnetic radiation with biological tissue we briefly recall existence and uniqueness theory associated with this problem then we show how a posteriori error indicators can be derived using an adjoint equation approach the error indicators use both the jump in normal and tangential components of the field across faces in the mesh

prediction error methods for limit cycle data prediction error methods are considered for identification of the forward linear dynamics of nonlinear feedback closed loop systems which operate in a perturbed stable limit cycle a model of the signals measured in a neighborhood of the limit cycle is presented and shown to satisfy a quasistationarity property quasistationarity is then used to prove that prediction error methods are both convergent and consistent for our data model

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

effect of noise and perturbations on limit cycle systems abstract this paper demonstrates that the influence of noise and of external perturbations on a nonlinear oscillator can vary strongly along the limit cycle and upon transition from limit cycle to stationary point behaviour for this purpose we consider the role of noise on the bonhoeffer van der pol model in a range of control parameters where the model exhibits a limit cycle but the parameters are close to values corresponding to a stable stationary point our analysis is based on the van kampen approximation for solutions of the fokker planck equation in the limit of weak noise we investigate first separately the effect of noise on motion tangential and normal to the limit cycle the key result is that noise induces diffusion like spread along the limit cycle but quasistationary behaviour normal to the limit cycle we then describe the coupled motion and show that noise acting in the normal direction can strongly enhance diffusion along the limit cycle we finally argue that the variability of the system s response to noise can be exploited in populations of nonlinear oscillators in that weak coupling can induce synchronization as long as the single oscillators operate in a regime close to the transition between oscillatory and excitatory modes

optimal harvesting policy of logistic population model in a randomly fluctuating environment abstract in this paper we investigate the optimal harvest policy of a stochastic logistic population model the value of this study lies in two aspects mathematically we establish a stochastic threshold theorem to govern whether the population persists or not in the case of population persistence we prove the existence uniqueness and global asymptotic stability of the invariant density of the fokker planck equation associated with the sde model and we further show the relation between these two models in addition we give the unique optimal harvesting effort and the corresponding maximum of expectation of sustainable yield which gives us the profile of the optimal harvesting policy of the sde model ecologically we find that big harvesting effort or big intensity of noise will lead the population to extinct risk almost surely in addition we find that under a fixed randomness strategy and proper harvesting the maximum sustainable yield increases systematically as the harvesting effort increases but overexploitation will reduce the level of maximize sustainable yield and eventually make the whole population extinct with probability one hence in order to obtain the optimal harvesting policy we must decrease the harvesting effort and the intensity of noise furthermore we find that our parameter perturbation method in this paper is more beneficial to the exploitation of renewable resources than the classical one given by beddington and may 1977 the results show that different perturbation method can exhibit different stochastic population dynamics

bifurcation analysis in an associative memory model we previously reported the chaos induced by the frustration of interaction in a nonmonotonic sequential associative memory model and showed the chaotic behaviors at absolute zero we have now analyzed bifurcation in a stochastic system namely a finite temperature model of the nonmonotonic sequential associative memory model we derived order parameter equations from the stochastic microscopic equations two parameter bifurcation diagrams obtained from those equations show the coexistence of attractors which do not appear at absolute zero and the disappearance of chaos due to the temperature effect

noise induced order a new noise effect on chaos in one dimensional mappings is reported the transition from chaotic behavior to ordered behavior induced by external noise is observed in a certain class of one dimensional mappings this transition is clearly shown in terms of the lyapunov number entropy power spectrum and the nature of orbits

stochastic hopf bifurcation in a biased van der pol model abstract the transient characteristics of a nonequilibrium phase transition is investigated in a model of abiased van der pol oscillator the state independent driving term which triggers the bifurcation from limit cycle to fixed point is treated as a randomly fluctuating quantity the advancement of the hopf bifurcation is explained as a result of noise induced periodicity found in this model system the phase boundary separating the two attractors is determined numerically and is interpreted as stochastic bifurcation locus in parameter space the phenomenon of critical slowing down occurring on the fixed point side is found to be similar to that which occurs in a deterministic system the relevent critical exponent is estimated to have the mean field value of unity irrespective of how the stochastic bifurcation points are approached in a two dimensional parameter space

attractors of convex maps with positive schwarzian derivative in the presence of noise abstract one dimensional maps have proved to be useful models for understanding the transition to turbulence we investigate a smooth perturbation of the well known logistic system in order to examine numerically the change in the bifurcation behavior which is observed when the schwarzian derivative is allowed to become positive we find coexistence of a fixed point attractor and a periodic or chaotic two band attractor the chaotic two band attractor can disappear by yielding a preturbulent state which will asymptotically settle down to a fixed point the chaotic behavior of some systems can be destroyed by arbitrarily small amounts of external noise the concept of diffusions is used to describe the sensitivity of attractors against external noise we also observe a direct transition from a fixed point to a chaotic one band attractor this can be interpreted as type iii intermittency of pomeau and manneville but with an almost linear scaling behavior of the lyapunov exponent

high order fdtd methods for transverse magnetic modes with dispersive interfaces a new finite difference time domain fdtd algorithm is introduced to solve two dimensional 2d transverse magnetic tm modes with a straight dispersive interface driven by the consideration of simplifying interface jump conditions the auxiliary differential equation of the debye constitution model is rewritten to form a new debye maxwell tm system interface auxiliary differential equations are utilized to describe the transient changes in the regularities of electromagnetic fields across a dispersive interface the resulting time dependent jump conditions are rigorously enforced in the fdtd discretization by means of a matched interface and boundary scheme higher order convergences are numerically achieved for the first time in the literature in 2d fdtd simulations of dispersive inhomogeneous media

a scaling theory of bifurcations in the symmetric weak noise escape problem we consider two dimensional overdamped double well systems perturbed by white noise in the weak noise limit the most probable fluctuational path leading from either point attractor to the separatrix the most probable escape path or mpep must terminate on the saddle between the two wells however as the parameters of a symmetric double well system are varied a unique mpep may bifurcate into two equally likely mpeps at the bifurcation point in parameter space the activation kinetics of the system become non arrhenius we quantify the non arrhenius behavior of a system at the bifurcation point by using the maslov wkb method to construct an approximation to the quasistationary probability distribution of the system that is valid in a boundary layer near the separatrix the approximation is a formal asymptotic solution of the smoluchowski equation our construction relies on a new scaling theory which yields critical exponents describing weak noise behavior at the bifurcation point near the saddle

non chaotic response of non linear oscillators under combined deterministic and weak stochastic excitations non linear oscillators under harmonic and or weak stochastic excitations are considered in this paper under harmonic excitations alone an analytical technique based on a set of exponential transformations followed by harmonic balancing is proposed to solve for a variety of one periodic orbits the stability boundaries for such orbits in the associated parameter space are constructed using the floquet theory under a combination of harmonic and weak stochastic excitations a stochastic perturbation approach around the deterministic orbit is adopted to obtain response statistics in terms of the evolving moment functions in the present study the stochastic perturbation is assumed to be an additive white noise process and equations for the evolving moments are derived using ito differential rule a fifth order cumulant neglect closure is used to close the infinite hierarchy of moment equations limited numerical results are presented to illustrate the implementation of the proposed scheme the method is found to be quite versatile and admits ready extensions to md o f systems under combined harmonic and white or non white multiplicative or additive random excitations

noise induced jumps in two coupled duffing oscillators abstract we consider two coupled duffing oscillators with the coexistence of four attractors switching between the coexisting attractors by noises is investigated three types of noises such as gaussian amplitude dependent and dichotomous are used we observed noise induced extrinsic intermittency intermittent dynamics is characterized using power spectrum average and relative residence times on each precoupled attractors and probability distribution of time interval between successive switchings variation of probability distribution of state variables in poincare map is studied as a function of noise strength the effect of various noises is compared the occurrence of crisis induced and type i intermittencies are also presented

ergodicity of randomly perturbed lorenz model we show by using the liapunov method that the lorenz model perturbed by gaussian white noise is ergodic for any rayleigh number our theory confirms two properties which have been found by numerical calculation we also discuss the ergodicity of some other randomly perturbed dissipative systems a one dimensional laser and a homopolar disk dynamo model of the geomagnetism

chaos and generalised multistability in a mesoscopic model of the electroencephalogram abstract we present evidence for chaos and generalised multistability in a mesoscopic model of the electroencephalogram eeg two limit cycle attractors and one chaotic attractor were found to coexist in a two dimensional plane of the ten dimensional volume of initial conditions the chaotic attractor was found to have a moderate value of the largest lyapunov exponent 3 4 s 1 base e with an associated kaplan yorke lyapunov dimension of 2 086 there are two different limit cycles appearing in conjunction with this particular chaotic attractor one multiperiodic low amplitude limit cycle whose largest spectral peak is within the alpha band 8 13 hz of the eeg and another multiperiodic large amplitude limit cycle which may correspond to epilepsy the cause of the coexistence of these structures is explained with a one parameter bifurcation analysis each attractor has a basin of differing complexity the large amplitude limit cycle has a basin relatively uncomplicated in its structure while the small amplitude limit cycle and chaotic attractor each have much more finely structured basins of attraction but none of the basin boundaries appear to be fractal the basins of attraction for the chaotic and small amplitude limit cycle dynamics apparently reside within each other we briefly discuss the implications of these findings in the context of theoretical attempts to understand the dynamics of brain function and behaviour

relations among subglottal pressure breathing and acoustic parameters of sentence level prominence in german this study investigates whether acoustic correlates of prominence are related to actions of the respiratory system resulting in local changes of subglottal pressure psub simultaneous recordings were made of acoustics intraoral pressure pio as an estimate of psub and thoracic and abdominal volume changes ten german speakers read sentences containing a verb ending with t followed by a noun starting with t these t t sequences were typically realized as one t with a long intraoral pressure plateau sentence level prominence was manipulated by shifting the position of contrastive focus within the sentences the slope and peak value of pio within the t t sequence was used to estimate differences in psub across focus positions results show that prominence production is related to changes in the slope and maximum value of the pressure plateau while pressure increases led to higher intensity they did not relate to f0 hence suggesting that local f0 changes primarily reflect laryngeal activity finally strong individual differences were observed in the respiratory data these findings confirm past reports of local psub increases corresponding to sentence level prominence speaker specific activations of the respiratory system are interpreted in terms of motor equivalence with laryngeal mechanisms also appearing to contribute to psub changes

spectral analysis of a nonlinear oscillator driven by random and periodic forces i linearized theory we have combined the techniques of statistical and harmonic linearization to develop a linearized approximation theory for the calculation of the second order statistics i e autocorrelation functions and spectral densities of nonlinear systems driven by both random and periodic forces for the special case of a duffing oscillator a damped anharmonic oscillator with a cubic nonlinearity driven by gaussian white noise and by a sinusoidal force explicit expressions for the renormalized linearized frequency the autocorrelation function and the spectral density of the oscillator displacement in terms of all the system parameters have been derived we have determined the region of the parameter space in which the applied periodic force has a significant influence on the second order statistics of the oscillator

variational bayesian identification and prediction of stochastic nonlinear dynamic causal models in this paper we describe a general variational bayesian approach for approximate inference on nonlinear stochastic dynamic models this scheme extends established approximate inference on hidden states to cover i nonlinear evolution and observation functions ii unknown parameters and precision hyperparameters and iii model comparison and prediction under uncertainty model identification or inversion entails the estimation of the marginal likelihood or evidence of a model this difficult integration problem can be finessed by optimising a free energy bound on the evidence using results from variational calculus this yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables we derive such a variational bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models for both model identification and time series prediction the computational complexity of the scheme is comparable to that of an extended kalman filter which is critical when inverting high dimensional models or long time series using monte carlo simulations we assess the estimation efficiency of this variational bayesian approach using three stochastic variants of chaotic dynamic systems we also demonstrate the model comparison capabilities of the method its self consistency and its predictive power

multistability and chaotic beating of duffing oscillators suspended on an elastic structure we consider the dynamics of a number of externally excited chaotic oscillators suspended on an elastic structure we show that for the given conditions of oscillations of the structure initially uncorrelated chaotic oscillators become periodic and synchronous in clusters in the periodic regime we have observed multistability as two or four different attractors coexist in each cluster a mismatch of the excitation frequency in the oscillators leads to the beating like behaviour we argue that the observed phenomena are generic in the parameter space and independent of the number of oscillators and their location on the elastic structure

analysis of excitability for the fitzhugh nagumo model via a stochastic sensitivity function technique we study excitability phenomena for the stochastically forced fitzhugh nagumo system modeling a neural activity noise induced changes in the dynamics of this model can be explained by the high stochastic sensitivity of its attractors computational methods based on the stochastic sensitivity functions technique are suggested for the analysis of these attractors our method allows us to construct confidence ellipses and estimate a threshold value of a noise intensity corresponding to the neuron excitement on the basis of the proposed technique a supersensitive limit cycle is found for the fitzhugh nagumo model