effect of colored noise on networks of nonlinear oscillators we discuss noise induced pattern formation in different two dimensional networks of nonlinear oscillators namely a sequence of biochemical reactions and the lorenz system the main focus of the work is on the dependence of these patterns on the correlation time i e the color of exponentially correlated gaussian noise it is seen that in the nonchaotic case the homogeneity or average cluster size goes through a minimum with higher correlation time while in its chaotic regime the lorenz system shows a higher degree of synchronization when the correlation time of the noise is increased in order to elucidate the origin of this phenomenon the effect of colored noise on the individual oscillator is investigated it is shown that the specific dependence of the network s homogeneity on the noise correlation time arises from an interplay of the collective behavior and the properties of the single oscillators doi 10 1103 physreve 64 021105

stochastic sensitivity of systems driven by colored noise abstract we study a response of the general nonlinear dynamic system to the colored noise a stochastic sensitivity analysis of equilibria forced by small exponentially correlated gaussian noise is carried out for the stochastic sensitivity matrix of the equilibrium a system of matrix equations is derived and explicit solution is found in 2d case applying these theoretical results we study a response of fitzhugh nagumo model to colored noise we analyze how dispersion of random states near the deterministic equilibrium depends on the characteristic time of the power limited colored noise the effect of the colored noise induced excitability is discussed

the degenerate parametric oscillator and ince s equation we construct green s function for the quantum degenerate parametric oscillator in the coordinate representation in terms of standard solutions of ince s equation in a framework of a general approach to variable quadratic hamiltonians exact time dependent wavefunctions and their connections with dynamical invariants and su 1 1 group are also discussed an extension to the degenerate parametric oscillator with time dependent amplitude and phase is also mentioned

the group theoretical treatment of aberrating systems iii the classification of asymmetric aberrations a lie theoretical classification of the aberrations of systems modeled by asymmetric optical devices is given the classification is done on the basis of aberration order and axial symmetry of the first order part this leads to finite dimensional nonunitary representations of sp 4 r reduced with respect to its sp 2 r subalgebra with helicity and symplectic spin labels based on pure magnifier systems a weight label reproduces and completes seidel s traditional classification of axis symmetric aberrations based on other first order systems such as optical fibers other classification schemes are indicated

unpredictable behavior in the duffing oscillator wada basins this paper describes some numerical experiments giving evidence of wada basin boundaries for the duffing oscillator we suggest some mechanisms by which this fractal property of the boundaries appears and discuss the difficulties that the wada property presents for predicting the behavior of dynamical systems

stochastic bifurcation for a tumor immune system with symmetric levy noise abstract in this paper we investigate stochastic bifurcation for a tumor immune system in the presence of a symmetric non gaussian levy noise stationary probability density functions will be numerically obtained to define stochastic bifurcation via the criteria of its qualitative change and bifurcation diagram at parameter plane is presented to illustrate the bifurcation analysis versus noise intensity and stability index the effects of both noise intensity and stability index on the average tumor population are also analyzed by simulation calculation we find that stochastic dynamics induced by gaussian and non gaussian levy noises are quite different

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

stability of stochastic levy noise coupled systems with mixed delays in this paper based on razumikhin method stability of stochastic levy noise coupled systems with mixed delays slcsd is researched here both mixed delays and levy noise are considered into cou

a new method of analysis of the effect of weak colored noise in nonlinear dynamical systems a systematic method for obtaining the asymptotic behavior of a dynamical system forced by colored noise in the limit of small intensity is developed it is based on the search of wkb solutions to the fokker planck equation for the joint probability density of the system and noise in which the perturbation expansion is continued to the first correction beyond the hamilton jacobi limit the method can be applied to noise with correlation time of order unity it is illustrated on the normal form of a pitchfork bifurcation where it is pointed out that additive noise can induce a shift of the most probable value this prediction is confirmed by numerical simulation of the stochastic differential equations

the heisenberg weyl group in the coherent state basis and the bargmann transform it is shown that the representation matrices of the quantum mechanical group in the coherent state basis can be used as bases for the expansion of arbitrary square integrable functions on the group although this basis is nonorthogonal the expansion can be inverted in a manner similar to an orthogonal basis next a coherent state wave function is defined in analogy with the schrodinger wave function and the above matrix elements are used to determine the action of the group in the space of the coherent state wave functions the function space in this realization is bargmann s hilbert space of analytic functions it is shown that the mixed basis matrix element between the coordinate and coherent state bases is essentially the integral kernel of bargmann the transpose of this matrix element yields the kernel for the inversion of the transform in this construction the bargmann transform appears as the unitary transformation connecting the schrodinger and coherent state wave functions this considerably

an angular momentum approach to quadratic fourier transform hadamard matrices gauss sums mutually unbiased bases the unitary group and the pauli group the construction of unitary operator bases in a finite dimensional hilbert space is reviewed through a nonstandard approach combining angular momentum theory and representation theory of su 2 a single formula for the bases is obtained from a polar decomposition of su 2 and is analyzed in terms of cyclic groups quadratic fourier transforms hadamard matrices and generalized gauss sums weyl pairs generalized pauli operators and their application to the unitary group and the pauli group naturally arise in this approach

stochastic bifurcations and coherencelike resonance in a self sustained bistable noisy oscillator we investigate the influence of additive gaussian white noise on two different bistable self sustained oscillators duffing van der pol oscillator with hard excitation and a model of a synthetic genetic oscillator in the deterministic case both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state we find that under the influence of noise their dynamics can be well characterized through the concept of stochastic bifurcation consisting in a qualitative change of the stationary amplitude distribution for the duffing van der pol oscillator analytical results obtained for a quasiharmonic approach are compared with the result of direct computer simulations in particular we show that the dynamics is different for isochronous and anisochronous systems moreover we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line this effect is similar to coherence resonance however in the case of anisochronous systems this effect breaks down and a new phenomenon anisochronous based stochastic bifurcation occurs

chaos noise and synchronization reconsidered in a recent paper maritan and banavar phys rev lett 72 1451 1994 reported the synchronization of identical chaotic systems by additive noise we relate such a synchronization to the maximum lyapunov exponent of a single system and discuss the underlying mechanisms of the effect in the case of the lorenz equations the nonvanishing mean of the noise mimics a parameter change leading to synchronization for the logistic map a state dependence of the fluctuations is induced by the boundary conditions

object grammars and bijections a new systematic approach for the specification of bijections between sets of combinatorial objects is presented it is based on the notion of object grammars object grammars give recursive descriptions of objects and generalize context free grammars the study of a particular substitution in these object grammars confirms once more the key role of dyck words in the domain of enumerative and bijective combinatorics

the phase transition in a bistable duffing system driven by levy noise in this paper the phase transition and mean first passage time mfpt induced by levy noise is investigated in a bistable duffing system numerically first we obtain the stationary probability density functions as the criterion of phase transition through the qualitative changes of the shapes of stationary probability distribution then the influences of levy noise parameters are discussed the results indicate that the stability index noise intensity and skewness parameter can lead to phase transition behaviors in bistable duffing system in addition the mfpt is calculated for various levy parameters different effects among stability index noise intensity and the skewness parameter on the phase transition and mfpt are observed furthermore distinctions between levy noise and gaussian noise are provided

normal form transforms separate slow and fast modes in stochastic dynamical systems modelling stochastic systems has many important applications normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from insignificant detailed microscale dynamics we explore such coordinate transforms of stochastic differential systems when the dynamics has both slow modes and quickly decaying modes the thrust is to derive normal forms useful for macroscopic modelling of complex stochastic microscopic systems thus we not only must reduce the dimensionality of the dynamics but also endeavour to separate emph all slow processes from emph all fast time processes both deterministic and stochastic quadratic stochastic effects in the fast modes contribute to the drift of the important slow modes some examples demonstrate that the coordinate transform may be only locally valid or may be globally valid depending upon the dynamical system the results will help us accurately model interpret and simulate multiscale stochastic systems

a class of affine wigner functions with extended covariance properties affine wigner functions are phase space representations based on the affine group in place of the usual weyl heisenberg group of quantum mechanics such representations are relevant to the time frequency analysis of real signals an interesting family is singled out by the requirement of covariance with respect to each solvable three parameter group containing the affine group explicit forms are given in each case and properties such as unitarity and localization are discussed some particular distributions are recovered

non symmetric forms of non linear vibrations of flexible cylindrical panels and plates under longitudinal load and additive white noise abstract parametric non linear vibrations of flexible cylindrical panels subjected to additive white noise are studied the governing marguerre equations are investigated using the finite difference method fdm of the second order accuracy and the runge kutta method the considered mechanical structural member is treated as a system of many infinite number of degrees of freedom dof the dependence of chaotic vibrations on the number of dofs is investigated reliability of results is guaranteed by comparing the results obtained using two qualitatively different methods to reduce the problem of pdes partial differential equations to odes ordinary differential equations i e the faedo galerkin method in higher approximations and the 4th and 6th order fdm the cauchy problem obtained by the fdm is eventually solved using the 4th order runge kutta methods the numerical experiment yielded for a certain set of parameters the non symmetric vibration modes forms with and without white noise in particular it has been illustrated and discussed that action of white noise on chaotic vibrations implies quasi periodicity whereas the previously non symmetric vibration modes are closer to symmetric ones

stochastic bifurcation in duffing van der pol oscillators global analysis of bifurcation in the duffing van der pol oscillators under both additive and multiplicative random excitations is explored in detail by the generalized cell mapping method using digraph system parameters are chosen in the range that two co exist attractors and a saddles as an alternative definition stochastic bifurcation may be defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value it is found that under certain conditions stochastic bifurcation always occurs when a stochastic attractor collides with a stochastic saddle our study reveals that the generalized cell mapping method with digraph is also a powerful tool for global analysis of stochastic bifurcation by this global analysis the mechanism of development occurrence and evolution of stochastic bifurcation can be explored clearly and vividly

invariants for the time dependent harmonic oscillator i two equivalent families of linear invariants and two equivalent families of quadratic invariants are obtained for a harmonic oscillator with variable mass or with variable frequency explicit formulae are obtained for the linear and quadratic invariants in the case of a damped oscillator and the hamiltonian is seen as a special quadratic invariant

antireliability of noise driven neurons we demonstrate within the framework of the fitzhugh nagumo model that a firing neuron can respond to a noisy driving in a nonreliable manner the same gaussian white noise acting on identical neurons evokes different patterns of spikes the effect is characterized via calculations of the lyapunov exponent and the event synchronization correlations we construct a theory that explains the antireliability as a combined effect of a high sensitivity to noise of some stages of the dynamics and nonisochronicity of oscillations geometrically the antireliability is described by a random noninvertible one dimensional map

the unitary irreducible representations of sl 2 r in all subgroup reductions we use the canonical transform realization of sl 2 r in order to find all matrix elements and integral kernels for the unitary irreducible representations of this group explicit results are given for all mixed bases and subgroup reductions these provide the full multiparameter set of integral transforms and series expansions associated to sl 2 r

the metaplectic group within the heisenberg weyl ring the heisenberg weyl ring contains the metaplectic group of canonical transforms acting unitarily on l 2 r these ring elements are characterized through i the integral transform kernels ii coset distributions and iii classical functions under any quantization scheme the isomorphism under group composition leads to several new relations involving twisted products and quantization of gaussian classical functions the wigner inversion operator is a special central group element it is shown that the only quantization scheme invariant under metaplectic transformations is the weyl scheme the structure studied here appears to be relevant to the study of wave optics with aberration

dynamics of limit cycle oscillators subject to general noise the phase description is a powerful tool for analyzing noisy limit cycle oscillators the method however has found only limited applications so far because the present theory is applicable only to gaussian noise while noise in the real world often has non gaussian statistics here we provide the phase reduction method for limit cycle oscillators subject to general colored and non gaussian noise including a heavy tailed one we derive quantifiers like mean frequency diffusion constant and the lyapunov exponent to confirm consistency of the results applying our results we additionally study a resonance between the phase and noise

on non autonomous dynamical systems in usual realistic classical dynamical systems the hamiltonian depends explicitly on time in this work a class of classical systems with time dependent nonlinear hamiltonians is analyzed this type of problems allows to find invariants by a family of veronese maps the motivation to develop this method results from the observation that the poisson lie algebra of monomials in the coordinates and momenta is clearly defined in terms of its brackets and leads naturally to an infinite linear set of differential equations under certain circumstances to perform explicit analytic and numerical calculations two examples are presented to estimate the trajectories the first given by a nonlinear problem and the second by a quadratic hamiltonian with three time dependent parameters in the nonlinear problem the veronese approach using jets is shown to be equivalent to a direct procedure using elliptic functions identities and linear invariants are constructed for the second example linear and quadratic invariants as well as stability conditions are given explicit solutions are also obtained for stepwise constant forces for the quadratic hamiltonian an appropriated set of coordinates relates the geometric setting to that of the three dimensional manifold of central conic sections it is shown further that the quantum mechanical problem of scattering in a superlattice leads to mathematically equivalent equations for the wave function if the classical time is replaced by the space coordinate along a superlattice the mathematical method used to compute the trajectories for stepwise constant parameters can be applied to both problems it is the standard method in quantum scattering calculations as known for locally periodic systems including a space dependent effective mass

linear transformations and aberrations in continuous and finite systems in geometric optics there is a natural distinction between the paraxial and aberration regimes which contain respectively the linear and nonlinear canonical transformations of position and momentum in the phase space in the lie theoretical presentation linear inhomogeneous transformations are generated by linear and quadratic functions of the phase space while aberrations of increasing order are generated by homogeneous functions with higher powers of these coordinates in a way parallel but distinct from the schrodinger quantization of continuous classical systems we quantize the geometric optical model into discrete finite dimensional systems based on the lie algebra whose wavefunctions are n point signals phase space is a sphere and transformations are represented by the n n unitary matrices that form the group we factor this group into linear and nonlinear unitary transformations of phase space and classify all its n2 4 aberrations this offers a new parametrization of based on a chosen subgroup

coherence enhancement in nonlinear systems subject to multiplicative ornstein uhlenbeck noise we show that for two biologically relevant models with self sustained oscillations under the action of a multiplicative ornstein uhlenbeck process their coherence response behaves nonmonotonically with the process correlation time there is a correlation time for which the quality factor is optimized this phenomenon is a consequence of the interplay between the correlation time and the system s periodicity this relation is evidenced through a power law relation with an exponent close to 1 2

colored noise induced hopf bifurcations in predator prey communities a broad class of n 1 species ratio dependent predator prey stochastic models which consist of one predator population and n prey populations is considered the effect of a fluctuating environment on the carrying capacities of prey populations is taken into account as colored noise in the framework of the mean field theory approximate self consistency equations for prey populations mean density and for predator population density are derived to the first order in the noise variance in some cases the mean field exhibits hopf bifurcations as a function of noise correlation time the corresponding transitions are found to be reentrant e g the periodic orbit appears above a critical value of the noise correlation time but disappears again at a higher value of the noise correlation time the nonmonotonous dependence of the critical control parameter on the noise correlation time is found and the conditions for the occurrence of hopf bifurcations are presented our results provide a possible scenario for environmental fluctuations induced transitions between the oscillatory regime and equilibrium state of population sizes observed in nature

the asymptotic stability of a noisy non linear oscillator abstract the purpose of this work is to obtain an approximation for the top lyapunov exponent the exponential growth rate of the response of a single well kramers oscillator driven by either a multiplicative or an additive white noise process to this end we consider the equations of motion as dissipative and noisy perturbations of a two dimensional hamiltonian system a perturbation approach is used to obtain explicit expressions for the exponent in the presence of small intensity noise and small dissipation we show analytically that the top lyapunov exponent is positive and for small values of noise intensity e and dissipation e the exponent grows in proportion with e1 3

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

non lorentzian spectral lineshapes near a hopf bifurcation the effects of additive white noise upon the dynamics of a system described by its hopf normal form are investigated with particular reference to the well known model of a detuned single mode laser the power spectrum corresponding to the laser amplitude is determined by finite difference solution of a partial differential equation and analytical formulas are determined in the asymptotic limits of large parameters the effect of the amplitude phase coupling parameter in generating non lorentzian lineshapes is highlighted and the regions of parameter space where accurate first eigenvalue approximations of the fokker planck equation exist are indicated

algebraic languages and polyominoes enumeration abstract in this paper the use of algebraic languages theory in solving an open problem in combinatorics is shown by constructing a bijection between convex polyominoes and words of an algebraic language and by solving the corresponding algebraic system we prove that the number of convex polyominoes with perimeter 2n 8 is 2n 11 4 n 4 2n 1 2n n

transition event duration in one dimensional systems under correlated noise abstract transition event duration ted is the spent time of a particle which enters a neighborhood of one state to reach another one without ever returning back to the state where it starts in this paper an approximate theoretical method is proposed to obtain the transition event duration distribution tedd of one dimensional bi stable strongly nonlinear systems under correlated noises it strongly extends the existing theoretical methods for obtaining the tedd actually an approximate theoretical solution of the tedd is determined by the fokker planck equation fpe with two absorbing boundary conditions here we set each absorbing boundary condition at stable and unstable points of a bi stable potential function firstly a solution to the fpe is presented by the c type gram charlier expansion subsequently based on the weighted residual scheme the fpe is reduced to a series of ordinary differential equations odes with unknown coefficient then an analytical solution to tedd is derived by solving this series of odes especially the concerning stochastic excitations of the system can be divided into five kinds of situations gaussian white noise colored gaussian noise two gaussian white noises with white cross correlation two gaussian white noises with exponential correlation and two colored gaussian noises with exponential correlation we mainly discuss the influences of correlation and the parameters of noise on the tedd our corresponding analytic results are compared with monte carlo simulations and good agreements are found

attribute grammars are useful for combinatorics abstract the purpose of this paper is to show the use of attribute grammars in solving some combinatorics problems for example we give the generating function for the shape of skew ferrers diagrams according to the number of cells and the number of columns this result is new and proves that skew ferrer diagrams are related to new basic bessel functions

phase diagram of the random frequency oscillator the case of ornstein uhlenbeck noise abstract we study the stability of a stochastic oscillator whose frequency is a random process with finite time memory represented by an ornstein uhlenbeck noise this system undergoes a noise induced bifurcation when the amplitude of the noise grows the critical curve that separates the absorbing phase from an extended non equilibrium steady state corresponds to the vanishing of the lyapunov exponent that measures the asymptotic logarithmic growth rate of the energy we derive various expressions for this lyapunov exponent by using different approximation schemes this allows us to study quantitatively the phase diagram of the random parametric oscillator

stationary energy probability density of oscillators driven by a random external force we derive rigorous analytical results for the stationary energy probability density function of linear and nonlinear oscillators driven by additive gaussian noise our study focuses on two cases i a harmonic oscillator subjected to gaussian colored noise with an arbitrary correlation function and ii nonlinear oscillators with a general potential driven by gaussian white noise we also derive analytical expressions for the stationary moments of the energy and investigate the partition of the mean energy between kinetic and potential energy to illustrate our general results we consider specifically the case of exponentially correlated noise for i and power law and bistable potentials for ii our theoretical results are substantiated by langevin simulations between the kinetic energy and the potential energy of the oscillator our studies focus on two cases first we consider a harmonically bound particle driven by general additive gaussian colored noise second we consider a particle in a general potential driven by gaussian white noise in both cases we develop a general theory and study specific illustrative examples the paper is organized as follows in sec ii we formulate the langevin equations for a particle with inertia in a general potential driven by an additive random force we also derive the general relation between the stationary energy pdf and the stationary pdf for the particle s position and velocity section iii is devoted to the motion of a particle in a harmonic potential driven by colored gaussian noise with an arbitrary correlation function the stationary energy pdf as well as the first and second moments of the energy is derived analytically we apply these results to the case of exponentially correlated gaussian noise and to gaussian white noise for these specific cases we also determine the partition of the energy between kinetic and potential energy we analyze the effect of the potential shape on the stationary energy pdf for oscillators driven by an additive gaussian white noise in sec iv w e apply our analytical results to two specific cases a general power law potential and a bistable potential the first type of oscillator without friction and with additive noise 36 and multiplicative noise 37 has recently been studied in the context of anomalous diffusion the second type the duffing oscillator has been investigated as an alternative to the linear oscillator for harvesting energy from external random sources 28 29 35 38 39

stochastic extinction and persistence of a parasite host epidemiological model abstract in this paper we investigate the stochastic extinction and persistence of a parasite host epidemiological model we show that the global dynamics of the stochastic model can be governed by the basic reproduction number r 0 s if r 0 s 1 under mild extra conditions the disease goes to extinction with probability one and the disease free dynamics occurs while r 0 s 1 under mild extra conditions the disease persists and endemic dynamics occurs almost surely the solutions of the stochastic model fluctuate around the steady state of the deterministic model and a unique stationary distribution can be found based on realistic parameters of daphnia microparasite system numerical simulations have been performed to verify extend our analytical results epidemiologically we find that 1 large environment fluctuations can suppress the outbreak of disease 2 the distributions are governed by r 0 s 3 the noise perturbations can be beneficial to control the spread of disease on average

the euclidean root of snell s law i geometric polarization optics coset spaces of the euclidean group of rigid motions in three space are used as a model of the rays in geometric polarization optics the haar measure invariance leads to canonicity of the phase space transformations the phase space of optical rays undergoes a canonical map also under the effect of smooth refracting or reflecting surfaces between two optical media that is governed by snell s law this is a conservation law between two irreducible representations of the euclidean group labeled by the refractive indices n n of the media these surface transformations are canonical and furthermore factorize into two root transformations that are also canonical this factorization applies equally to the transformation of the polarization vector the root transformation permits the computation of an aberration expansion of the polarization field over the object screen the generators of infinitesimal surface transformations are found i e those that transform between media n and n dn it is shown that

stochastic hopf bifurcation the effect of colored noise on the bifurcation interval we consider a general nonlinear dynamical system undergoing a supercritical hopf bifurcation and driven by a gaussian colored noise using normal form theory and an approximate effective fokker planck equation valid for weak intensity and small correlation time of the noise we obtain an explicit expression for the stationary probability distribution of the full general system close to the bifurcation and analyze the changes in the shape of the distribution to discuss the effect of the noise on the bifurcation interval textcopyright 1996 the american physical society

self induced stochastic resonance in excitable systems the effect of small amplitude noise on excitable systems with strong time scale separation is analyzed it is found that vanishingly small random perturbations of the fast excitatory variable may result in the onset of a deterministic limit cycle behavior absent without noise the mechanism termed self induced stochastic resonance combines a stochastic resonance type phenomenon with an intrinsic mechanism of reset and no periodic drive of the system is required self induced stochastic resonance is different from other types of noise induced coherent behaviors in that it arises away from bifurcation thresholds in a parameter regime where the zero noise deterministic dynamics does not display a limit cycle nor even its precursor the period of the limit cycle created by the noise has a non trivial dependence on the noise amplitude and the time scale ratio between fast excitatory variables and slow recovery variables it is argued that self induced stochastic resonance may offer one possible scenario of how noise can robustly control the function of biological systems

a stochastic sis epidemic model with vaccination abstract in this paper we investigate the basic features of an sis type infectious disease model with varying population size and vaccinations in presence of environment noise by applying the markov semigroup theory we propose a stochastic reproduction number r 0 s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence if r 0 s 1 under some mild extra conditions there exists a disease free absorbing set for the stochastic epidemic model which implies that disease dies out with probability one while if r 0 s 1 under some mild extra conditions the sde model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease the most interesting finding is that large environmental noise can suppress the outbreak of the disease

the zeros of basic bessel functions the functions jv ax x and associated orthogonal polynomials abstract the modified lommel polynomials are generalized and their orthogonality relation is obtained as a byproduct we prove that the non zero roots of jv ax x are real simple and interlace with those of jv ax 1 x the q lommel polynomials are shown to play in the theory of basic bessel function the role played by the lommel polynomials in the bessel function theory the q lommel polynomials are proved to be orthogonal with respect to a purely discrete measure with bounded support this is then used to prove that the prositive zeros of x j 2 v x q are real simple and interlace with the zeros of x 1j 2 v 1 x q when 1 we also establish the complete monotonicity of 1x 1 2 j v 1 2 i x q j v 2 i x q

simultaneous influence of additive and multiplicative noise on stationary dissipative solitons we investigate the simultaneous influence of spatially homogeneous multiplicative noise as well as of spatially correlated additive noise on the formation of localized patterns in the framework of the cubic quintic complex ginzburg landau equation depending on the ratio between the strength of additive and multiplicative noise we find a number of distinctly different types of behavior including explosions collapse filling in and spatio temporal disorder as well as intermittent behavior of all types listed techniques used to analyze the results include snapshots x t plots and plots of the spatially and temporally averaged amplitude as a function of the strength of multiplicative noise while keeping the strength of additive noise fixed typically 50 realizations are used for averaging to obtain the corresponding data points in these diagrams for the widths of these distribution as a function of additive noise we obtain a linear decrease in the limit of fairly large but fixed values of the multiplicative noise to summarize our findings concisely we show three dimensional plots of the mean pattern amplitude and the generalized susceptibility as a function of the strengths of additive and multiplicative noise we critically compare the results of our investigations with those obtained in the two limiting cases of purely additive and of purely multiplicative noise

variations on a theme of heisenberg pauli and weyl the parentage between weyl pairs the generalized pauli group and the unitary group is investigated in detail we start from an abstract definition of the heisenberg weyl group on the field and then switch to the discrete heisenberg weyl group or generalized pauli group on a finite ring the main characteristics of the latter group an abstract group of order d3 noted pd are given conjugacy classes and irreducible representation classes or equivalently lie algebra of dimension d3 associated with pd leaving the abstract sector a set of weyl pairs in dimension d is derived from a polar decomposition of su 2 closely connected to angular momentum theory then a realization of the generalized pauli group pd and the construction of generalized pauli matrices in dimension d are revisited in terms of weyl pairs finally the lie algebra of the unitary group u d is obtained as a subalgebra of the lie algebra associated with pd this leads to a development of the lie algebra of u d in a basis consisting of d2 generalized pauli matrices in the case where d is a power of a prime integer the lie algebra of su d can be decomposed into d 1 cartan subalgebras

riccati equations and lie series lie series and a special matrix notation for first order differential operators are used to show that the lie group properties of matrix riccati equations arise in a natural way the lie series notation makes it evident that the solutions of a matrix riccati equation are curves in a group of nonlinear transformations that is a generalization of the linear fractional transformations familiar from the classical complex analysis it is easy to obtain a linear representation of the lie algebra of the nonlinear group of transformations and then this linearization leads directly to the standard linearization of the matrix riccati equations we note that the matrix riccati equations considered here are of the general rectangular type

response probability density functions of duffing van der pol vibro impact system under correlated gaussian white noise excitations abstract this paper aims to investigate the stationary probability density functions pdfs of a duffing van der pol vibro impact system excited by correlated gaussian white noise with the help of non smooth transformation the stationary pdfs are formulated analytically by the stochastic averaging of energy envelope the analytical results are verified by numerical simulation results stochastic bifurcations for different parameters are considered and several special pdf forms are observed in this paper the first form is the shape of the pdf of total energy can be similar to a crater which has a minimum and a maximum the second one is the shape of the joint pdf with three peaks that is to say the section of joint pdf has three maximum and two minimum in addition the influence of the degree of the correlation of gaussian white noises is explored

stability measures in metastable states with gaussian colored noise we present a study of the escape time from a metastable state of an overdamped brownian particle in the presence of colored noise generated by ornstein uhlenbeck process we analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity we observe the noise enhanced stability effect for all the initial unstable states used and for all values of the correlation time tau c investigated we can distinguish two dynamical regimes characterized by weak and strong correlated noises depending on the value of tau c with respect to the relaxation time of the system

stochastic bifurcations in a bistable duffing van der pol oscillator with colored noise this paper aims to investigate gaussian colored noise induced stochastic bifurcations and the dynamical influence of correlation time and noise intensity in a bistable duffing van der pol oscillator by using the stochastic averaging method theoretically one can obtain the stationary probability density function of amplitude for the duffing van der pol oscillator and can reveal interesting dynamics under the influence of gaussian colored noise stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution which indicates that system parameters noise intensity and noise correlation time respectively can be treated as bifurcation parameters they also imply that the effects of multiplicative noise are rather different from that of additive noise the results of direct numerical simulation verify the effectiveness of the theoretical analysis moreover the largest lyapunov exponent calculations indicate that p and d bifurcations have no direct connection

modified kramers formulas for the decay rate in agreement with dynamical modeling abstract accuracy of the kramers approximate formulas for the thermal decay rate of the metastable state is studied for the anharmonic shapes of the potential pocket and the barrier this is done by the comparison with the quasistationary rate resulting from the dynamical modeling disagreement between the kramers rate and the dynamical one is shown to reach 15 in the cases when much better agreement is expected corrections to the kramers formulas accounting for the higher derivatives of the potential are obtained the small parameters are the ratios of the thermal energy to the stiffnesses at the extremes of the potential the distance between the potential barrier and the absorptive border is accounted for as well this corrected kramers rate is demonstrated to agree with the dynamical rate typically within 2 probably the most interesting result is that despite the corrections are derived in the case of the overdamped brownian motion the above 2 agreement holds even in the case of medium friction

noise induced convergence of the low flow rate chaos in the belousov zhabotinsky reaction abstract the effect of noise on the low flow rate chaos in the belousov zhabotinsky bz reaction was studied the chaos was simulated using the three variable model of gyorgyi and field gaussian white noise was imposed on the flow rate of the reactant solutions fed into cstr to simulate the so called type p noise the range of average noise amplitudes was chosen between 0 01 and 1 related to the inverse residence time the calculated time series were analyzed on the basis of their fourier spectra maximum lyapunov exponent kolmogorov entropies return maps and invariant density we found that the noise induces partial order of the period 3 like oscillations in the low flowrate chaos

time dependent potentials associated with exceptional orthogonal polynomials we introduce a method for generating rational extensions of time dependent potentials such that the associated schrodinger equation admits solutions in terms of exceptional orthogonal polynomials our method is applicable to position dependent schrodinger equations as well as to their conventional counterparts for constant mass

stochastic dynamics of michaelis menten kinetics based tumor immune interactions abstract in this paper we investigate deterministic and stochastic dynamics of michaelis menten kinetics based tumor immune interactions for the deterministic case stability analysis is performed by routh hurwitz criteria chaos is observed in bifurcation analysis and examined by the method of 0 1 test the stochastic system is constructed by incorporating multiplicative white noise terms into the deterministic system we establish a unique positive solution ensuring the positiveness and boundedness of solution from the positive initial condition the sufficient condition is obtained for weak persistence in mean we also derive the parametric restrictions for stochastic permanence and global attractivity in mean finally we validate the extinction of tumor cells with the transition from co existence domain by crossing the estimated threshold values of intensity of environmental noise

levy flight random searches in biological phenomena abstract there has been growing interest in the study of levy flights observed in the movements of biological organisms performing random walks while searching for other organisms here we approach the problem of what is the best statistical strategy for optimizing the encounter rate between searcher and target organisms either of the same or of different species in terms of a limiting generalized searcher target model e g predator prey mating partner pollinator flower in this context we discuss known results showing that for fixed targets an inverse square density distribution of step lengths can optimize the encounter rate for moving targets we review how the encounter rate depends on whether organisms move in levy or brownian random walks we discuss recent findings indicating that levy walks confer a significant advantage for increasing encounter rates only when the searcher is larger or moves rapidly relative to the target and when the target density is low

stochastic bifurcation in a driven laser system experiment and theory we analyze the effects of stochastic perturbations in a physical example occurring as a higher dimensional dynamical system the physical model is that of a class b laser which is perturbed stochastically with finite noise the effect of the noise perturbations on the dynamics is shown to change the qualitative nature of the dynamics experimentally from a stochastic periodic attractor to one of chaoslike behavior or noise induced chaos to analyze the qualitative change we apply the technique of the stochastic frobenius perron operator l billings et al phys rev lett 88 234101 2002 to a model of the experimental system our main result is the identification of a global mechanism to induce chaoslike behavior by adding stochastic perturbations in a realistic model system of an optics experiment in quantifying the stochastic bifurcation we have computed a transition matrix describing the probability of transport from one region of phase space to another which approximates the stochastic frobenius perron operator this mechanism depends on both the standard deviation of the noise and the global topology of the system our result pinpoints regions of stochastic transport whereby topological deterministic dynamics subjected to sufficient noise results in noise induced chaos in both theory and experiment

positive lyapunov exponents in the kramers oscillator the maximum lyapunov exponent is computed numerically for the double well oscillator in a heat bath positive exponents are found in a wide range of friction coefficients in the low damping regime

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

zero dispersion stochastic resonance a new form of stochastic resonance sr discovered in underdamped nonlinear oscillators for which the dependence of eigenfrequency upon energy has an extremum is investigated its characteristic features are identified and discussed on the basis of linear response theory and the fluctuation dissipation theorem in common with conventional sr in bistable systems sharp increases in the response to a weak periodic force and in the signal noise ratio occur with increasing intensity of external noise temperature within a certain range unlike conventional sr however the dependence of the response on frequency is strongly resonant

experimental evidence of stochastic resonance without tuning due to non gaussian noises in order to test theoretical predictions we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non gaussian noise in agreement with the theoretical predictions our main findings are an enhancement of the sensibility of the system together with a remarkable widening of the response robustness this implies that even a single resonant unit can reach a marked reduction in the need for noise tuning

multiple scales scheme for bifurcation in a delayed extended van der pol oscillator abstract the van der pol vdp oscillator is an essential nonlinear oscillator which has been extensively studied however the results of delayed generalized vdp oscillator are relatively less the issue of bifurcation control for a delayed extended vdp oscillator is fully considered in this paper firstly a nonlinear time delayed feedback controller is carefully designed to control the dynamics for the proposed oscillator and the results of stability of such oscillator are obtained by means of stability switches theory secondly a general explicit formula is derived to establish the properties of hopf bifurcation by utilizing the method of multiple scales moreover the impact of feedback gain on the bifurcation point for the controlled oscillator is demonstrated numerically finally the effectiveness of theoretical results is verified via a numerical example

stochastic bifurcation in noise driven lasers and hopf oscillators this paper considers nonlinear dynamics in an ensemble of uncoupled lasers each being a limit cycle oscillator which are driven by the same external white gaussian noise as the external noise strength increases there is an onset of synchronization and then subsequent loss of synchrony local analysis of the laser equations shows that synchronization becomes unstable via stochastic bifurcation to chaos defined as a passing of the largest lyapunov exponent through zero the locus of this bifurcation is calculated in the three dimensional parameter space defined by the hopf parameter amount of amplitude phase coupling and external noise strength numerical comparison between the laser system and the normal form of hopf bifurcation uncovers a square root law for this stochastic bifurcation as well as strong enhancement in noise induced chaos due to the laser s relaxation oscillation

characterizing the robustness and susceptibility of steady state dynamics in post buckled structures to stochastic perturbations abstract recent reports exemplify both the potential and the concerns encountered in implementing post buckled structures in diverse applications by numerical and experimental methods characterizations have provided useful insights on the dynamic sensitivities of such bi or multistable structures subjected to either harmonic or stochastic excitations yet the more realistic scenario of combined harmonic and stochastic loading has been not been closely examined so that such sensitivities might be fully illuminated to provide a more complete understanding on the robustness and susceptibility of multistable structures to dynamic state transitions this research establishes new analytical and experimental methods to quantify the likelihood of triggering transitions among dynamic regimes of an archetypal post buckled structure as a result of combined harmonic and stochastic loading it is discovered that persistent periodic snap through dynamics are rapidly disabled by additional noise excitation when the harmonic excitation contribution occurs at frequencies close to the linearized resonance the extra noise may also drastically compromise the integrity of small amplitude periodic responses that occur at frequencies around one half of the linearized resonance particular relative proportions of the noise standard deviation and harmonic excitation amplitude are uncovered that most readily compromise the robustness of a given steady state dynamic regime the analytical method also complements prior developments focused on stochastic resonance by uncovering the broader perspective of dynamic sensitivities of post buckled structures under arbitrary combinations of harmonic and random driving loads

a deterministic and stochastic model for the system dynamics of tumor immune responses to chemotherapy abstract modern medical studies show that chemotherapy can help most cancer patients especially for those diagnosed early to stabilize their disease conditions from months to years which means the population of tumor cells remained nearly unchanged in quite a long time after fighting against immune system and drugs in order to better understand the dynamics of tumor immune responses under chemotherapy deterministic and stochastic differential equation models are constructed to characterize the dynamical change of tumor cells and immune cells in this paper the basic dynamical properties such as boundedness existence and stability of equilibrium points are investigated in the deterministic model extended stochastic models include stochastic differential equations sdes model and continuous time markov chain ctmc model which accounts for the variability in cellular reproduction growth and death interspecific competitions and immune response to chemotherapy the ctmc model is harnessed to estimate the extinction probability of tumor cells numerical simulations are performed which confirms the obtained theoretical results

from object grammars to eco systems in this paper we make a comparison between two methods for the enumeration of combinatorial objects namely the eco method and object grammars both based on a recursive description for the examined class of objects in particular we study the problem of passing from an object grammar to an equivalent eco system first we solve this problem for any unidimensional unambiguous and complete object grammar with any linear parameter then we treat the more complex cases of q linear parameters and of multidimensional object grammars giving some explanatory examples in particular we determine a new eco system for the class of directed convex polyominoes

the group theoretical treatment of aberrating systems i aligned lens systems in third aberration order the constituents of a lens system i e slabs of homogeneous transparent material and the refracting surfaces between them considered to third aberration order are associated to elements of a nine parameter aberration group three parameters correspond to gaussian systems and six to group classified aberrations the group multiplication operation through matrix cum vector algebra corresponds to their concatenation and the linear group action on an eight dimensional homogeneous space corresponds to the nonlinear action of the system on the optical phase space this leads to economical computation algorithms that may be extended to aberrating systems of higher order

characterization of escape times of josephson junctions for signal detection the measurement of the escape time of a josephson junction might be used to detect the presence of a sinusoidal signal embedded in noise when use of standard signal processing tools can be prohibitive due to the extreme weakness of the source or to the huge amount of data in this paper we show that the prescriptions for the experimental setup and some physical behaviors depend on the detection strategy more specifically by exploitation of the sample mean of escape times to perform detection two resonant regions are identified at low frequencies there is a stochastic resonance or activation phenomenon while near the plasma frequency a geometric resonance appears furthermore detection performance in the geometric resonance region is maximized at the prescribed value of the bias current the naive sample mean detector is outperformed in terms of error probability by the optimal likelihood ratio test the latter exhibits only geometric resonance showing monotonically increasing performance as the bias current approaches the junction critical current in this regime the escape times are vanishingly small and therefore performance is essentially limited by measurement electronics the behavior of the likelihood ratio and sample mean detector for different values of incoming signal to noise ratio is discussed and a relationship with the error probability is found detectors based on the likelihood ratio test could be employed also to estimate unknown parameters in the applied input signal as a prototypical example we study the phase estimation problem of a sinusoidal current which is accomplished by using the filter bank approach finally we show that for a physically feasible detector the performances are found to be very close to the cramer rao theoretical bound applications might be found for example in some astronomical detection problems where the all sky gravitational and or radio wave search for pulsars requires the analysis of nearly sinusoidal long lived waveforms at very low signal to noise ratio or to analyze weak signals in the subterahertz range where the traditional electronics counterpart is difficult to implement

effects of a periodic drive and correlated noise on birhythmic van der pol systems abstract this paper considers the dynamics of a van der pol birhythmic oscillator submitted both to colored noise and harmonic excitation applying the quasi harmonic assumption to the corresponding langevin equation we derive an approximated fokker planck equation that is compared with the results of computer simulations we thus derive both the effects of the correlation time and the harmonic excitation on the parameter space where birhythmicity appears in this region we find that the multi limit cycle van der pol oscillator reduces to an asymmetric bistable system where the sinusoidal drive intensity plays the role of asymmetric parameter and noise can lead to stochastic bifurcations consisting in a qualitative change of the stationary amplitude distribution under both influence of noise and harmonic excitation the dynamics can be well characterized through the concepts of pseudo potential that regulates the low noise arrhenius like behavior

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

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

stability of a stochastic two dimensional non hamiltonian system we study the top lyapunov exponent of the response of a two dimensional non hamiltonian system driven by additive white noise the origin is not a fixed point for the system however there is an invariant measure for the one point motion of the system in this paper we consider the stability of the two point motion by khasminskii s method of linearization along trajectories the specific system we consider is the third order truncated normal form of the unfolding of a hopf bifurcation we show that in the small noise limit the top lyapunov exponent always approaches zero from below and is thus negative for noise sufficiently small we also show that there exist open sets of parameters for which the top lyapunov exponent is positive thus the two point motion can be either stable or unstable while the stationary density that describes the one point motion always exists

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

transitions induced by cross correlated bounded noises and time delay in a genotype selection model abstract we present a numerical investigation of occurrence of transitions in a genotype selection model with time delay where two bounded noises are cross correlated stationary probability distribution spd function is obtained it is found that the multiplicative bounded noise can facilitate the gene separation and it plays a constructive role in the genetic selection progress while the additive bounded noise suppresses the gene separation the strong correlation between noises gives a big chance to one type haploid out of the group besides what is more interesting is that the correlation time can induce a new transitions i e the curve of the spd changes from unimodal to bimodal and then to four peaks as the correlation time increases

quantization symmetry and natural polarization we discuss the notion of polarization as defined in a geometric quantization scheme recently introduced in terms of the role played by the evolution operator of the quantum system the analysis uses an integral transform representation of the group wsp 2 r this clarifies the group theoretic origin of the natural polarizations and the meaning of the polarization changing transformations

synchronization and desynchronization of self sustained oscillators by common noise we consider the effect of external noise on the dynamics of limit cycle oscillators the lyapunov exponent becomes negative under influence of small white noise what means synchronization of two or more identical systems subject to common noise we analytically study the effect of small nonidentities in the oscillators and in the noise and derive statistical characteristics of deviations from the perfect synchrony large white noise can lead to desynchronization of oscillators provided they are nonisochronous this is demonstrated for the van der pol duffing system

on an involution on dyck paths les derniers resultats concernant l enumeration des polyamines parallelogrammes 4 5 8 9 11 14 selon l aire et le nombre de colonnes font apparaitre des fonctions generatrices s exprimant comme rapport de q analogues de fonctions de bessel dans 13 deux interpretations combinatoires de ces memes fonctions sont donnees d une part en termes de multiparcours d arbres et d autre part en termes de multichaines de chemins de dyck a l aide d une involution sur l ensemble d des chemins de dyck d une bijection entre chemins et multiparcours d arbres et d une bijection entre chemins et multichaines nous donnons dans ce papier une preuve bijective de l equivalence de ces deux interpretations

numerical methods for the mean exit time and escape probability of two dimensional stochastic dynamical systems with non gaussian noises the mean exit time and escape probability are deterministic quantities that can quantify dynamical behaviors of stochastic differential equations with non gaussian stable type levy motions both deterministic quantities are characterized by differential integral equations i e differential equations with nonlocal terms but with different exterior conditions a convergent numerical scheme is developed and validated for computing the mean exit time and escape probability for two dimensional stochastic systems with rotationally symmetric stable type levy motions the effects of drift gaussian noises intensity of jump measure and domain sizes on the mean exit time are discussed the difference between the one dimensional and two dimensional cases is also presented

sensitivity of a hopf bifurcation to multiplicative colored noise the location of a hopf bifurcation in parameter space may be postponed or advanced by multiplicative colored noise depending on the interplay between the time scale of the noise and the rotation period of the phase variable

co existing responses and stochastic resonance in post buckled structures a combined numerical and experimental study abstract much of what is known about co existing responses in nonlinear systems under both deterministic and random dynamic loading is limited to phenomenological investigations of discrete systems most commonly the duffing equation from these results alone it is difficult to extrapolate the behavior of the distributed nonlinear systems more commonly seen in real structures such as buckled beams and curved panels this is because beyond the simple increase in dimension real systems bring with them imperfections and more complex forms of energy dissipation the possibility of co existing responses particularly in the case of simultaneous safe and unsafe solutions e g snap through and non snap through poses potential problems for engineers as it multiplies the workload since one must be very careful to ensure that a particular simulation or experiment has captured the most critical response even in the case where random forces dominate the overall loading of a system a situation in which one might anticipate an equally random response a very small harmonic component can have an influence beyond its proportion this effect known as stochastic resonance is quite counterintuitive to the analyst more familiar with linear systems where the principles of superposition and scalar multiplication of solutions make this impossible in this paper the effect of the damping and noise level on the number of co existing responses in nonlinear systems is investigated stochastic resonance is also demonstrated first with a double well duffing oscillator and then it is shown to exist experimentally we believe for the first time on a macroscopic structure that being an imperfect buckled beam

on time dependent quadratic quantum hamiltonians we apply the techniques of canonical transforms to equations of the type left a t mathbb p 2 b t mathbb p mathbb q mathbb q mathbb p c t mathbb q 2 d t mathbb q e t mathbb p f t mathbb 1 right psi q t i partial t psi q t where mathbb q and mathbb p are the quantum position and momentum operators the time dependent parameters of the text w wedge text sl text 2 r evolution operator are found through linear differential equations in terms of these we give explicitly the green s function all separating coordinates and similarity solutions of the equation we analyze the behavior of gaussian and coherent state initial conditions in closed form and present a new interpretation of all the lewis riesenfeld constants of motion

the properties of the anti tumor model with coupling non gaussian noise and gaussian colored noise abstract the anti tumor model with correlation between multiplicative non gaussian noise and additive gaussian colored noise has been investigated in this paper the behaviors of the stationary probability distribution demonstrate that the multiplicative non gaussian noise plays a dual role in the development of tumor and an appropriate additive gaussian colored noise can lead to a minimum of the mean value of tumor cell population the mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states an increase in both the non gaussian noise intensity and the departure from the gaussian noise can accelerate the transition from the disease state to the healthy state on the contrary an increase in cross correlated degree will slow down the transition moreover the correlation time can enhance the stability of the disease state

stochastic resonance of a periodically driven neuron under non gaussian noise abstract we investigate the first passage time statistics of the integrate fire neuron model driven by a sub threshold harmonic signal superposed with a non gaussian noise here we considered the noise as the result of a random multiplicative process displaced from the origin by an additive term such a mechanism generates a power law distributed noise whose characteristic decay exponent can be finely tuned we performed numerical simulations to analyze the influence of the noise non gaussian character on the stochastic resonance condition we found that when the noise deviates from gaussian statistics the resonance condition occurs at weaker noise intensities achieving a minimum at a finite value of the distribution function decay exponent we discuss the possible relevance of this feature to the efficiency of the firing dynamics of biological neurons as the present result indicates that neurons would require a lower noise level to detect a sub threshold signal when its statistics departs from gaussian