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The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at $(mN_c+1)$-th oscillators…
In this paper, we investigate synchronization of coupled second-order linear harmonic oscillators with random noises and time delays. The interaction topology is modeled by a weighted directed graph and the weights are perturbed by white…
Motivated by synchronization problems in noisy environments, we study the Edwards-Wilkinson process on weighted uncorrelated scale-free networks. We consider a specific form of the weights, where the strength (and the associated cost) of a…
In this article, we study algorithms for dynamic networks with asynchronous start, i.e., each node may start running the algorithm in a different round. Inactive nodes transmit only heartbeats, which contain no information but can be…
In this Letter we identify the general rules that determine the synchronization properties of interconnected networks. We study analytically, numerically and experimentally how the degree of the nodes through which two networks are…
We study optimal synchronization in networks of heterogeneous phase oscillators. Our main result is the derivation of a synchrony alignment function that encodes the interplay between network structure and oscillators' frequencies and can…
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…
We study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized…
We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is…
This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived.…
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…
We assess the power consumption of network synchronisation protocols, particularly the energy required to synchronise all nodes across a network. We use the widely adopted approach of bio-inspired, pulse-coupled oscillators to achieve…
Today, complex networks have attracted increasing attention from various fields of science and engineering. It has been demonstrated that many complex networks display various synchronization phenomena. In this paper, we introduce a…
By numerical simulations, we investigate the onset of synchronization of networked phase oscillators under two different weighting schemes. In scheme-I, the link weights are correlated to the product of the degrees of the connected nodes,…
We present exact results, as well as some illustrative Monte Carlo simulations, concerning a stochastic network with weighted connections in which the fraction of nodes that are dynamically synchronized is a parameter. This allows one to…
We consider complete synchronization of identical maps coupled through a general interaction function and in a general network topology where the edges may be directed and may carry both positive and negative weights. We define mixed…
Synchronization of identical harmonic oscillators interconnected via position, velocity, and acceleration couplings is studied. How to construct a complex Laplacian matrix representing the overall coupling is presented. It is shown that the…
The role of restorative coupling on synchronization of coupled identical harmonic oscillators is studied. Necessary and sufficient conditions, under which the individual systems' solutions converge to a common trajectory, are presented.…