Related papers: Global synchronization theorem for coupled swarmal…
We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary…
Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the…
In this paper, we investigate the development of generalized synchronization (GS) on typical complex networks, such as scale-free networks, small-world networks, random networks and modular networks. By adopting the auxiliary-system…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…
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)…
The collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied when the natural frequency distribution does not possess an even symmetry with respect to the average natural frequency…
We quantify the dynamical implications of the small-world phenomenon. We consider the generic synchronization of oscillator networks of arbitrary topology, and link the linear stability of the synchronous state to an algebraic condition of…
Clock synchronization is a widely discussed topic in the engineering literature. Ensuring that individual clocks are closely aligned is important in network systems, since the correct timing of various events in a network is usually…
This paper gives sufficient conditions for having complete synchronization of oscillators in connected undirected networks. The considered oscillators are not necessarily identical and the synchronization terms can be nonlinear. An…
In this paper, inspired by the idea that many real networks are composed by different sorts of communities, we investigate the synchronization property of oscillators on such networks. We identify the communities by the intrinsic…
Globally coupled phase oscillator models, such as the Kuramoto model, exhibit spontaneous collective synchronization. Such models can be restated in terms of interactions within and between subsets of oscillators. An approximation for the…
Imagine a group of oscillators, each endowed with their own rhythm or frequency, be it the ticking of a biological clock, the swing of a pendulum, or the glowing of fireflies. While these individual oscillators may seem independent of one…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
We study the collective behavior of swarmalators, generalizations of phase oscillators that both sync and swarm, confined to move on a 1D ring. This simple model captures some of the essence of movement in 2D or 3D but has the benefit of…
Synchronization of coupled oscillators is a ubiquitous phenomenon found throughout nature. Its robust realization is crucial to our understanding of various nonlinear systems, ranging from biological functions to electrical engineering. On…
Synchronization in the networks of coupled oscillators is a widely studied topic in different areas. It is well-known that synchronization occurs if the connectivity of the network dominates heterogeneity of the oscillators. Despite…
We give a succinct and self-contained description of the synchronized motion on networks of mutually coupled oscillators. Usually, the stability criterion for the stability of synchronized motion is obtained in terms of Lyapunov exponents.…
The importance of pulse-coupled oscillators (PCOs) in biology and engineering has motivated research to understand basic properties of PCO networks. Despite the large body of work addressing PCOs, a global synchronization result for…
In this article I investigate the novel synchronization behaviors of evolving pulse-coupled oscillator networks. Unlike previous models, the time-varying mechanism is inspired by neural network development, where seldom used links die out…
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…