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There are rich emergent phase behaviors in non-equilibrium active systems. Flocking and clustering are two representative dynamic phases. The relationship between these two phases is still unclear. In the paper, we numerically investigate…

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…

In the first part of this paper, we showed that three coupled populations of identical phase oscillators give rise to heteroclinic cycles between invariant sets where populations show distinct frequencies. Here, we now give explicit…

We consider an array of units each of which can be in one of three states. Unidirectional transitions between these states are governed by Markovian rate processes.The interactions between units occur through a dependence of the transition…

We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled…

Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two…

We prove the existence of a multi-dimensional non-trivial invariant toroidal manifold for the Kuramoto network with adaptive coupling. The constructed invariant manifold corresponds to the multi-cluster behavior of the oscillators phases.…

We experimentally demonstrate the occurrence of various synchronized states in coupled piece-wise linear time-delayed electronic circuits using dynamic environment coupling where the environment has its own intrinsic dynamics via feedback…

This work introduces a methodology for studying synchronization in adaptive networks with heterogeneous plasticity (adaptation) rules. As a paradigmatic model, we consider a network of adaptively coupled phase oscillators with…

Using recent dimensionality reduction techniques in large systems of coupled phase oscillators exhibiting bistability, we analyze complex macroscopic behavior arising when the coupling between oscillators is allowed to evolve slowly as a…

Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…

This paper addresses the behavior of large systems of heterogeneous, globally coupled oscillators each of which is described by the generic Landau-Stuart equation, which incorporates both phase and amplitude dynamics of individual…

We investigate a system of four nearest neighbour bidirectional coupled phase oscillators of dissimilar initial frequencies in a ring at the changeover into a synchronizing state. There are twenty four permutations upon assigning the…

Understanding how higher-order interactions affect collective behavior is a central problem in nonlinear dynamics and complex systems. Most works have focused on a single higher-order coupling function, neglecting other viable choices. Here…

The phenomenon of slow switching in populations of globally coupled oscillators is discussed. This characteristic collective dynamics, which was first discovered in a particular class of the phase oscillator model, is a result of the…

Inspired by Axelrod's model of culture dissemination, we introduce and analyze a model for a population of coupled oscillators where different levels of synchronization can be assimilated to different degrees of cultural organization. The…

We investigate an array of identical phase oscillators non-locally coupled without time delay, and find that chimera state with two coherent clusters exists which is only reported in delay-coupled systems previously. Moreover, we find that…

We examine microscopic mechanisms for coupling stochastic oscillators so that they display similar and correlated temporal variations. Unlike oscillatory motion in deterministic dynamical systems, complete synchronization of stochastic…

We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…

Ensembles of coupled nonlinear oscillators are a popular paradigm and an ideal benchmark for analyzing complex collective behaviors. The onset of cluster synchronization is found to be at the core of various technological and biological…