Related papers: Stochastic Resonance in Maps and Coupled Map Latti…
We investigate the collective signal response of two typical nonlinear dynamical models, the mean-field coupled overdamped bistable oscillators and the underdamped Duffing oscillators, with respect to both the additive Ornstein-Uhlenbeck…
The problem of a linear damped noisy oscillator is treated in the presence of two multiplicative sources of noise which imply a random mass and random damping. The additive noise and the noise in the damping are responsible for an influx of…
We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that underlying the stochastic…
Recent massive numerical simulations have shown that the response of a "stochastic resonator" is enhanced as a consequence of spatial coupling. Similar results have been analytically obtained in a reaction-diffusion model, using…
The effect of multiplicative white noise on the resonance capture in non-isochronous systems with time-decaying pumping is investigated. It is assumed that the intensity of perturbations decays with time, and its frequency is asymptotically…
We consider a damped $\beta$-Fermi-Pasta-Ulam chain, driven at one boundary subjected to stochastic noise. It is shown that, for a fixed driving amplitude and frequency, increasing the noise intensity, the system's energy resonantly…
We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that…
We show the existence of internal stochastic resonance in a microscopic stochastic model for the oscillating CO oxidation on single crystal surfaces. This stochastic resonance arises directly from the elementary reaction steps of the system…
The dynamics of a system formed by a finite number $N$ of globally coupled bistable oscillators and driven by external forces is studied focusing on a global variable defined as the arithmetic mean of each oscillator variable. Several…
It is shown that nonlocal coupling provides for controlling the collective noise-induced dynamics in the regime of stochastic resonance. This effect is demonstrated by means of numerical simulation on an example of coupled overdamped…
We study theoretically a bistable systems with time-delayed feedback driven by weak periodic force. The effective potential function and the steady-state probability density are derived. The delay time and the strength of its feedback can…
We present simple classical dynamical models to address the question of introducing a stochastic nature in a time variable. These models include noise in the time variable but not in the "space" variable, which is opposite to the normal…
This work is about the synchronization of nonlinear coupled dynamical systems driven by $\alpha$-stable noise. Firstly, we provide a novel technique to construct the relationship between synchronized system and slow-fast system. Secondly,…
Theory of nonlinear resonance, including stochastic one, is developed on the basis of the statistical field theory and using variables action-angle. Explicit expressions of action, proper frequency and nonlinearity parameter as functions of…
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check,…
We study the spatial distributions of two randomly interacting species, in the presence of an external multiplicative colored noise. The dynamics of the ecosystem is described by a coupled map lattice model. We find a nonmonotonic behavior…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
Chaos and Noise are ubiquitous in the Brain. Inspired by the chaotic firing of neurons and the constructive role of noise in neuronal models, we for the first time connect chaos, noise and learning. In this paper, we demonstrate Stochastic…
We investigate the resonance type behaviour of an overdamped Brownian particle in a bistable potential driven by external periodic signal. It has been shown previously that the input energy pumped into the system by the external drive shows…
The generic linear evolution of the density matrix of a system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear…