Related papers: Classification of synchronization in nonlinear sys…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network…
Synchronization is central to many complex systems in engineering physics (e.g., the power-grid, Josephson junction circuits, and electro-chemical oscillators) and biology (e.g., neuronal, circadian, and cardiac rhythms). Despite these…
The particular properties of synchronization are discussed for coupled auto-oscillating systems, which are characterized by non-quadratic law of potential dependence on the coordinate. In particular, structure of the parameter plane…
The full dynamics of a synchronous recurrent neural network model with Ising binary units and a Hebbian learning rule with a finite self-interaction is studied in order to determine the stability to synaptic and stochastic noise of…
We experimentally demonstrate group synchrony in a network of four nonlinear optoelectronic oscillators with time-delayed coupling. We divide the nodes into two groups of two each, by giving each group different parameters and by enabling…
The present study proposes a methodology that combines the 'Duffing oscillator system' and the 'Kuramoto oscillator network' to explore the synchronization of weak signals in dynamic systems. The first step of the procedure is to detect…
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…
We propose a theoretical framework to study the cooperative behavior of dynamically coupled oscillators (DCOs) that possess dynamical interactions. Then, to understand synchronization phenomena in networks of interneurons which possess…
A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear…
After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: deterministic coupling and common forcing. The inclusion of independent random forcing in these models typically…
The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system…
The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear transformation of coordinates and velocities. This is a rather…
A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of…
We propose a basic mechanism for isochronal synchrony and communication with mutually delay-coupled chaotic systems. We show that two Ikeda ring oscillators (IROs), mutually coupled with a propagation delay, synchronize isochronally when…
We study synchronization of nonlinear systems that satisfy an incremental passivity property. We consider the case where the control input is subject to a class of disturbances, including constant and sinusoidal disturbances with unknown…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of…
We explore both analytically and numerically an ensemble of coupled phase-oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time-delay (due to finite signal-propagation…
The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We show that synchronization can be achieved even for harmonic oscillators that are bilinearly coupled via a purely…