Related papers: Bifurcation Analysis of Noise-induced Synchronizat…
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…
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,…
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed…
Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We classify bifurcations of the critical set (the equilibria of the…
Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…
In this work, we analyse the effect of adding Gaussian white noise to the slow variable of a slow--fast system passing through a saddle--node (or fold) bifurcation. This problem is mainly motivated by applications to non-equilibrium energy…
Two types of synchronization, Achronal Synchronization and Isochronous synchronization are investigated numerically when unidirectionally coupled laser systems are considered both on fast and slow dynamics by studying the correlation…
We report a noise induced delay of bifurcation in a simple pulse-coupled neural circuit. We study the behavior of two neural oscillators, each individually governed by saddle-node dynamics, with reciprocal excitatory synaptic connections.…
Motivated by a stochastic differential equation describing the dynamics of interfaces, we study the bifurcation behavior of a more general class of such equations. These equations are characterized by a 2-dimensional phase space (describing…
We study synchronization in large populations of coupled phase oscillators with time-delays, higher order interactions. With each of these effects individually giving rise to bistabiltiy between incoherence and synchronization via a…
Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…
We study synchronization processes in networks of slightly non identical chaotic systems, for which a complete invariant synchronization manifold does not rigorously exist. We show and quantify how a slightly dispersed distribution in…
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…
A geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise. We show that the emergence of cooperative behaviour through a change of stability…
An analysis of transition from chaotic to nonchaotic behavior and synchronization in an ensemble of systems driven by identical random forces is presented. The synchronization phenomenon is investigated in the ensemble of particles moving…
Conditions such as insomnia, cardiac arrhythmia and jet-lag share a common feature: they are all related to the ability of biological systems to synchronize with the day-night cycle. When organisms lose resilience, this ability of…
The usual interpretation of noise is represented by a sum of many independent two-level elementary random signals with a distribution of relaxation times. In this paper it is demonstrated that also the superposition of many similar…
This paper investigates synchronization phenomena in networks of coupled oscillators governed by three-time-scale dynamical systems exhibiting canard dynamics. A mathematical framework has been developed to analyze the synchronization of…
We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…
From the flashes of fireflies to Josephson junctions and power infrastructure, networks of coupled phase oscillators provide a powerful framework to describe synchronization phenomena in many natural and engineered systems. Most real-world…