Related papers: Stochastic bifurcations: a perturbative study
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
Stochastic resonance phenomenon induced by non-Gaussian L\'evy noise in a second-order bistable system is investigated. The signal-noise-ratio for different parameters is computed by an efficient numerical scheme. The influences of the…
Noise aids the encoding of continuous signals into pulse sequences by way of stochastic resonance and endows the encoding device with a preferred frequency. We study encoding by a threshold device based on the Ornstein-Uhlenbeck process,…
The mechanism of the exponential transient statistics of Poincar\'e recurrences in the presence of chaos border with its critical structure is studied using two simple models: separatrix map and the kicked rotator ('microtron'). For the…
We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an…
We apply the Linear Delta Expansion (LDE) to the Lindstedt-Poincare (``distorted time'') method to find improved approximate solutions to nonlinear problems. We find that our method works very well for a wide range of parameters in the case…
Using algorithms of Higuchi and of Grassberger and Procaccia, we study numerically how fractal dimensions cross over from finite-dimensional Brownian noise at short time scales to finite values of deterministic chaos at longer time scales…
The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincar\'e recurrence time has been extensively used to characterize nonlinear dynamical…
This paper is devoted to investigating the random dynamics of stochastic discrete long-wave-short-wave resonance equations, which are characterized by the following features: $(1)$ the equations contain locally Lipschitz nonlinear coupling…
Slowing down phenomena occur in both deterministic and stochastic dynamical systems at the vicinity of phase transitions or bifurcations. An example is found in systems exhibiting a saddle-node bifurcation, which undergo a dramatic time…
We study the kinetic Fokker-Planck equation perturbed by a stochastic Vlasov force term. When the noise intensity is not too large, we solve the Cauchy Problem in a class of well-localized (in velocity) functions. We also show that, when…
An alternative perturbative expansion in quantum mechanics which allows a full expression of the scaling arbitrariness is introduced. This expansion is examined in the case of the anharmonic oscillator and is conveniently resummed using a…
We have analyzed the interplay between noise and periodic spatial modulations in bistable systems outside equilibrium and found that noise is able to increase the spatial order of the system, giving rise to periodic patterns which otherwise…
The one-dimensional motion of any number $\cN$ of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener…
We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focussing on the dependance of the instability threshold on the mass. For multiplicative noise in the damping, the instability…
A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf shall be investigated. Our purpose will be to analyze the…
We present the numerical estimation of noise parameter induced in the dynamics of the variables by random particle interactions involved in the stochastic chemical oscillator and use it as order parameter to detect the transition from…
This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…
We consider the long-time behavior of systems close to a system with a smooth first integral. Under certain assumptions, the limiting behavior, to some extent, turns out to be universal: it is determined by the first integral, the…
We present a study of disorder origination and growth inside an ordered phase processes induced by the presence of multiplicative noise within mean-field approximation. Our research is based on the study of solutions of the nonlinear…