Related papers: Coupled nonlinear stochastic differential equation…
Stochastic resonance holds much promise for the detection of weak signals in the presence of relatively loud noise. Following the discovery of nondynamical and of aperiodic stochastic resonance, it was recently shown that the phenomenon can…
Constructing discrete models of stochastic partial differential equations is very delicate. Stochastic centre manifold theory provides novel support for coarse grained, macroscale, spatial discretisations of nonlinear stochastic partial…
A stochastic averaging technique based on energy-dependent frequency is extended to dynamical systems with triple-well potential driven by colored noise. The key procedure is the derivation of energy-dependent frequency according to the…
Nonreciprocal coupling can alter the transport properties of material media, producing striking phenomena such as unidirectional amplification of waves, boundary modes, or self-assembled pattern formation. It is responsible for nonlinear…
In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying first the nonlocal SPDEs and showing then the convergence of the family of these…
We study the noisy dynamics of two coupled bistable modes of a nanomechanical beam. When de-coupled, each driven mode obeys the Duffing equation of motion, with a well-defined bistable region in the frequency domain. When both modes are…
A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain a Langevin type…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
In this paper we consider the global stability of solutions of an affine stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…
We consider a non-linear filtering problem, whereby the signal obeys the stochastic Navier-Stokes equations and is observed through a linear mapping with additive noise. The setup is relevant to data assimilation for numerical weather…
In this paper, we establish existence and uniqueness of strong solutions for a stochastic differential equation driven by an additive noise given by the sum of two correlated fractional Brownian sheets with different Hurst parameters. Our…
We study the asymptotic behaviour of different statistics for time series exhibiting long memory and nonstationarity. For processes with memory parameter $d\in(-1/2,3/2)$, we derive the joint limiting distribution of discrete Fourier…
We study the effects of noise cross-correlations on the steady states of driven, nonequilibrium systems, which are described by two stochastically driven dynamical variables, in one dimension. We use a well-known stochastically driven…
We present a class of systems for which the signal-to-noise ratio always increases when increasing the noise and diverges at infinite noise level. This new phenomenon is a direct consequence of the existence of a scaling law for the…
In this paper it is demonstrated that 1/f power spectrum appears in the process originated by the superposition of many single-sided random telegraph signals (RTS or RTN) with the same amplitude, probability and relaxation time. Indeed, the…
Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Covariance of the resulting probabilities requires the "anti-Ito" sense. The corresponding Fokker-Planck equation is simplified and preserves important features of the case with a constant diffusion. Multiplicative noise can always be…
This paper studies the stability properties of stochastic differential equations subject to persistent noise (including the case of additive noise), which is noise that is present even at the equilibria of the underlying differential…