Four-cluster chimera state in non-locally coupled phase oscillator systems with an external potential

Dynamics of a one-dimensional array of non-locally coupled Kuramoto phase oscillators with an external potential is studied. A four-cluster chimera state is observed for the moderate strength of the external potential. Different from the clustered chimera states studied before, the instantaneous frequencies of the oscillators in a synchronized cluster are different in the presence of the external potential. As the strength of the external potential increases, a bifurcation from the two-cluster chimera state to the four-cluster chimera states can be found. These phenomena are well predicted analytically with the help of the Ott-Antonsen ansatz.

Explosive synchronization:From synthetic to real-world networks

Synchronization is a widespread phenomenon in both synthetic and real-world networks.This collective behavior of simple and complex systems has been attracting much research during the last decades.Two different routes to synchrony are defined in networks;first-order,characterized as explosive,and second-order,characterized as continuous transition.Although pioneer researches explained that the transition type is a generic feature in the networks,recent studies proposed some frameworks in which different phase and even chaotic oscillators exhibit explosive synchronization.The relationship between the structural properties of the network and the dynamical features of the oscillators is mainly proclaimed because some of these frameworks show abrupt transitions.Despite different theoretical analyses about the appearance of the firstorder transition,studies are limited to the mean-field theory,which cannot be generalized to all networks.There are different real-world and man-made networks whose properties can be characterized in terms of explosive synchronization,e.g.,the transition from unconsciousness to wakefulness in the brain and spontaneous synchronization of power-grid networks.In this review article,explosive synchronization is discussed from two main aspects.First,pioneer articles are categorized from the dynamical-structural framework point of view.Then,articles that considered different oscillators in the explosive synchronization frameworks are studied.In this article,the main focus is on the explosive synchronization in networks with chaotic and neuronal oscillators.Also,efforts have been made to consider the recent articles which proposed new frameworks of explosive synchronization.

Synchronization of second-order Kuramoto networks from the perspective of edge dynamics

This paper presents new synchronization conditions for second-order phase-coupled Kuramoto oscillators in terms of edge dynamics.Two types of network-underlying graphs are studied,the positively weighted and signed graphs,respectively.We apply an edge Laplacian matrix for a positively weighted network to represent the edge connections.The properties of the edge Laplacian matrix are analyzed and incorporated into the proposed conditions.These conditions take account of the dynamics of edge-connected oscillators instead of all oscillator pairs in conventional studies.For a network with positive and negative weights,we represent the network by its spanning tree dynamics,and derive conditions to evaluate the synchronization state of this network.These conditions show that if all edge weights in the spanning tree are positive,and the tree-induced dynamics are in a dominant position over the negative edge dynamics,then this network achieves synchronization.The theoretical findings are validated by numerical examples.

Synchronization of Phase Oscillators in Networks with Certain Frequency Sequence

Synchronization of Kuramoto phase oscillators arranged in real complex neural networks is investigated. It is shown that the synchronization greatly depends on the sets of natural frequencies of the involved oscillators. The influence of network connectivity heterogeneity on synchronization depends particularly on the correlation between natural frequencies and node degrees. This finding implies a potential application that inhibiting the effects caused by the changes of network structure can be bManced out nicely by choosing the correlation parameter appropriately.