Related papers: The persistence of synchronization under $\alpha$-…
We demonstrate that waves in distinct layers of a neuronal network can become phase-locked by common spatiotemporal noise. This phenomenon is studied for stationary bumps, traveling waves, and breathers. A weak noise expansion is used to…
Synchronization of chaos arises between coupled dynamical systems and is very well understood as a temporal phenomena which leads the coupled systems to converge or develop a dependence with time. In this work, we provide a complementary…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
We illustrate a counter-intuitive effect of an additive stochastic force, which acts independently on each element of an ensemble of globally coupled oscillators. We show numerically and semi-analytically that a very small white noise is…
Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation and theory. However, complex systems in engineering and science are often subject to non-Gaussian fluctuations or uncertainties. A coupled…
We analyze the noise induced synchronization between a collective variable characterizing a complex system with a finite number of interacting bistable units and time periodic driving forces. A random phase process associated to the…
We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective…
A basic result in synchronization of linear systems via output coupling is presented. For identical discrete-time linear systems that are detectable from their outputs and neutrally stable, it is shown that a linear output feedback law…
We provide sufficient conditions for weak synchronization by noise for order-preserving random dynamical systems on Polish spaces. That is, under these conditions we prove the existence of a weak point attractor consisting of a single…
We consider the synchronization of the solutions to coupled stochastic systems of $N$-stochastic ordinary differential equations (SODEs) driven by Non-Gaussian L\'evy noises ($N\in \mathbb{N})$. We discuss the synchronization between two…
The paper addresses the synchronization of multi-agent systems with continuous-time dynamics interacting through a very general class of monotonic continuous signal functions that covers estimation biases, approximation of discrete…
In this letter a new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops with random precession frequencies. The model allows for an explicit study of orientational effects in…
Stochastic averaging problems with Gaussian forcing have been studied thoroughly for many years, but far less attention has been paid to problems where the stochastic forcing has infinite variance, such as an {\alpha}-stable noise forcing.…
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…
In this paper, we characterize the synchronization phenomenon of hyperchaotic scalar non-linear delay dynamics in a fully-developed chaos regime. Our results rely on the observation that, in that regime, the stationary statistical…
In this paper, we study asynchronous stochastic approximation algorithms without communication delays. Our main contribution is a stability proof for these algorithms that extends a method of Borkar and Meyn by accommodating more general…
We investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked, overdamped bistable potential driven by white Gaussian noise, the archetype description of Stochastic Resonance. We present a…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
We present analytical and numerical results on the joint dynamics of two coupled Duffing oscillators with nonlinearity of opposite signs (hardening and softening). In particular, we focus on the existence and stability of synchronized…
A synchronization mechanism driven by annealed noise is studied for two replicas of a coupled-map lattice which exhibits stable chaos (SC), i.e. irregular behavior despite a negative Lyapunov spectrum. We show that the observed…