Related papers: Synchronization of dissipative dynamical systems d…
We study the effect of common noise on coupled active rotators. While such a noise always facilitates synchrony, coupling may be attractive or repulsing. We develop an analytical approach based on a transformation to approximate…
We study an extended system that without noise shows a monostable dynamics, but when submitted to an adequate multiplicative noise, an effective bistable dynamics arise. The stochastic resonance between the attractors of the…
This paper investigates a damped stochastic wave equation driven by a non-Gaussian Levy noise. The weak solution is proved to exist and be unique. Moreover we show the existence of a unique invariant measure associated with the transition…
We introduce a new characteristics of chaoticity of classical and quantum dynamical systems by defining the notion of the dissipation time which enables us to test how the system responds to the noise and in particular to measure the speed…
Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase…
In this paper, we derive several criteria for (weak) synchronization by noise without the global swift transitivity property. Our sufficient conditions for (weak) synchronization are necessary and can be applied to scenarios involving…
Generalized synchronization between coupled dynamical systems is a phenomenon of relevance in applications that range from secure communications to physiological modelling. Here we test the capabilities of reservoir computing and, in…
We study the dynamics of a simple adaptive system in the presence of noise and periodic damping. The system is composed by two paths connecting a source and a sink, the dynamics is governed by equations that usually describe food search of…
Synchronization of coupled dynamical systems is a widespread phenomenon in both biological and engineered networks, and understanding this behavior is crucial for controlling such systems. Considerable research has been dedicated to…
Two identical 1D autocatalytic systems with Gray--Scott kinetics--driven towards convectively unstable regimes and submitted to independent spatiotemporal Gaussian white noises--are coupled unidirectionally, but otherwise linearly.…
We review some recent work on the synchronization of coupled dynamical systems on a variety of networks. When nodes show synchronized behaviour, two interesting phenomena can be observed. First, there are some nodes of the floating type…
We consider a dynamical system in R driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Levy noise of small intensity and such that the heaviest tail…
We show that in driven systems the Gaussian nature of the fluctuating force and time-reversibility are equivalent properties. This result together with the potential condition of the external force drastically restricts the form of the…
We study the interplay between non-Hermitian dynamics and phase synchronization in a system of $\mathcal{N}$ bosonic modes coupled to an auxiliary mode. The linearity of the evolution in such a system allows for the derivation of fully…
In this paper we present a generalized analytical solution to the generalized state equations of coupled second-order non-autonomous circuit systems. The analytical solutions thus obtained are used to study the synchronization dynamics of…
Synchronization of coupled continuous-time linear systems is studied in a general setting. For identical neutrally-stable linear systems that are detectable from their outputs, it is shown that a linear output feedback law exists under…
We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators…
The paper deals with the problem of long-time asymptotic behaviour of solutions for classes of ODEs and PDEs, perturbed by stationary noises. The latter are not assumed to be $\delta$-correlated in time, so that the evolution in question is…
Phase oscillator systems with global sine-coupling are known to exhibit low-dimensional dynamics. In this paper, such characteristics are extended to phase oscillator systems driven by Cauchy noise. The low-dimensional dynamics solution…
We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…