Related papers: The persistence of synchronization under $\alpha$-…
We solve the generalized Langevin equation driven by a stochastic force with power-law autocorrelation function. A stationary Markov process has been applied as a model of the noise. However, the resulting velocity variance does not…
In this paper, we study a system of stochastic partial differential equations with slow and fast time-scales, where the slow component is a stochastic real Ginzburg-Landau equation and the fast component is a stochastic reaction-diffusion…
This paper is concerned with the study of synchronization and consensus phenomena in complex networks of diffusively-coupled nodes subject to external disturbances. Specifically, we make use of stochastic Lyapunov functions to provide…
We consider two coupled phase oscillators in the presence of proportional ("common") and independent white noises. The global synchronization properties of the system are analytically studied via the Fokker-Planck equation. When the…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
A model for synchronization of globally coupled phase oscillators including ``inertial'' effects is analyzed. In such a model, both oscillator frequencies and phases evolve in time. Stationary solutions include incoherent (unsynchronized)…
Synchronization is a widespread phenomenon encountered in many natural and engineered systems with nonlinear classical dynamics. How synchronization concepts and mechanisms transfer to the quantum realm and whether features are universal or…
We study two coupled discrete-time equations with different (asynchronous) periodic time scales. The coupling is of the type sample and hold, i.e., the state of each equation is sampled at its update times and held until it is read as an…
Stochastic resonance (SR) is a prominent phenomenon in many natural and engineered noisy system, whereby the response to a periodic forcing is greatly amplified when the intensity of the noise is tuned to within a specific range of values.…
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…
We study the statistical physics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show…
Previous studies on oscillator populations with two-simplex interaction have reported novel phenomena such as discontinuous desynchronization transitions and multistability of synchronized states. However, the noise effect is not well…
The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…
The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of…
We propose here a stochastic binary element whose transition rate depends on its state at a fixed interval in the past. With this delayed stochastic transition this is one of the simplest dynamical models under the influence of ``noise''…
A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient…
We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise…
Synchronization is shown to occur in spatially extended systems under the effect of additive spatio-temporal noise. In analogy to low dimensional systems, synchronized states are observable only if the maximum Lyapunov exponent $\Lambda$ is…
Experiments that discuss influence of noise to H. Seidel and H. Herzel dynamics model of human cardiovascular system are presented. Noise is introduced by considering stochastic delays in response to the sympathetic system. It appears that…
Combined action of noise and deterministic force in dynamical systems can induce resonant effects. Here, we demonstrate a minimal, deterministic-force-free, setup allowing for occurrence of resonant, noise induced effects. We show that in…