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A scenario has recently been reported in which in order to stabilize complete synchronization of an oscillator network---a symmetric state---the symmetry of the system itself has to be broken by making the oscillators nonidentical. But how…
Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a…
We propose a simple and new unified method to achieve lag, complete and anticipatory synchronizations in coupled nonlinear systems. It can be considered as an alternative to the subsystem and intentional parameter mismatch methods. This…
Networks of limit cycle oscillators can show intricate patterns of synchronization such as splay states and cluster synchronization. Here we analyze dynamical states that display a continuum of seemingly independent splay clusters. Each…
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…
Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…
Biological neural networks exist in physical space where distance influences communication delays: a fundamental coupling between space and time absent in most artificial neural networks. While recent work has separately explored spatial…
We study a model of binary decisions in a fully connected network of interacting agents. Individual decisions are determined by social influence, coming from direct interactions with neighbours, and a group level pressure that accounts for…
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…
We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the…
We show that for large coupling delays the synchronizability of delay-coupled networks of identical units relates in a simple way to the spectral properties of the network topology. The master stability function used to determine stability…
We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another…
Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay…
We compare asynchronous vs. synchronous update of discrete dynamical networks and find that a simple time delay in the nodes may induce a reproducible deterministic dynamics even in the case of asynchronous update in random order. In…
It is known that an identical delay in all transmission lines can destabilize macroscopic stationarity of a neural network, causing oscillation or chaos. We analyze the collective dynamics of a network whose intra-transmission delays are…
Swarmalators are a class of coupled oscillators that simultaneously synchronize in both space and phase, providing a minimal model for systems ranging from biological microswimmers to robotic swarms. Time delay is ubiquitous in such…
Zero-lag synchronization (ZLS) is achieved in a very restricted mutually coupled chaotic systems, where the delays of the self-coupling and the mutual coupling are identical or fulfil some restricted ratios. Using a set of multiple…
Synaptic, dendritic and single-cell kinetics generate significant time delays that shape the dynamics of large networks of spiking neurons. Previous work has shown that such effective delays can be taken into account with a rate model…
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 study impact of multiplexing on the global phase synchronizability of different layers in the delayed coupled multiplex networks. We find that at strong couplings, the multiplexing induces the global synchronization in sparse networks.…