Reviving oscillation with optimal spatial period of frequency distribution in coupled oscillators

Inferring synchronizability of networked heterogeneous oscillators with machine learning

In the study of network synchronization, an outstanding question of both theoretical and practical significance is how to allocate a given set of heterogeneous oscillators on a complex network in order to improve the synchronization performance. Whereas methods have been proposed to address this question in the literature, the methods are all based on accurate models describing the system dynamics, which, however, are normally unavailable in realistic situations. Here, we show that this question can be addressed by the model-free technique of a feed-forward neural network (FNN) in machine learning. Specifically, we measure the synchronization performance of a number of allocation schemes and use the measured data to train a machine. It is found that the trained machine is able to not only infer the synchronization performance of any new allocation scheme, but also find from a huge amount of candidates the optimal allocation scheme for synchronization.

The impact of propagation and processing delays on amplitude and oscillation deaths in the presence of symmetry-breaking coupling

We numerically investigate the impacts of both propagation and processing delays on the emergences of amplitude death (AD) and oscillation death (OD) in one system of two Stuart-Landau oscillators with symmetry-breaking coupling. In either the absence of or the presence of propagation delay, the processing delay destabilizes both AD and OD by revoking the stability of the stable homogenous and inhomogenous steady states. In the AD to OD transition, the processing delay destabilizes first OD from large values of coupling strength until its stable regime completely disappears and then AD from both the upper and lower bounds of the stable coupling interval. Our numerical study sheds new insight lights on the understanding of nontrivial effects of time delays on dynamic activity of coupled nonlinear systems.

Introduction to focus issue: Patterns of network synchronization

The study of synchronization of coupled systems is currently undergoing a major surge fueled by recent discoveries of new forms of collective dynamics and the development of techniques to characterize a myriad of new patterns of network synchronization. This includes chimera states, phenomena determined by symmetry, remote synchronization, and asymmetry-induced synchronization. This Focus Issue presents a selection of contributions at the forefront of these developments, to which this introduction is intended to offer an up-to-date foundation.