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Eigenvector-based analysis of cluster synchronization in general complex networks of coupled chaotic oscillators

Frontiers of physics 2023年第4期18卷 321-335页

作者： Huawei Fan Ya Wang Xingang Wang School of Science Xi’an University of Posts and TelecommunicationsXi’an 710121China School of Physics and Information Technology Shaanxi Normal UniversityXi’an 710062China

Whereas topological symmetries have been recognized as crucially important to the exploration of synchronization patterns in complex networks of coupled dynamical oscillators,the identification of the symmetries in largesize complex networks remains as a challenge.Additionally,even though the topological symmetries of a complex network are known,it is still not clear how the system dynamics is transited among different synchronization patterns with respect to the coupling strength of the oscillators.We propose here the framework of eigenvector-based analysis to identify the synchronization patterns in the general complex networks and,incorporating the conventional method of eigenvalue-based analysis,investigate the emergence and transition of the cluster synchronization states.We are able to argue and demonstrate that,without a prior knowledge of the network symmetries,the method is able to predict not only all the cluster synchronization states observable in the network,but also the critical couplings where the states become stable and the sequence of these states in the process of synchronization transition.The efficacy and generality of the proposed method are verified by different network models of coupled chaotic oscillators,including artificial networks of perfect symmetries and empirical networks of non-perfect symmetries.The new framework paves a way to the investigation of synchronization patterns in large-size,general complex networks.

关键词： cluster synchronization complex networks network symmetry coupled oscillators

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Synchronization within synchronization: transients and intermittency in ecological networks

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National Science Review 2021年第10期8卷 23-32页

作者： Huawei Fan Ling-Wei Kong Xingang Wang Alan Hastings Ying-Cheng Lai School of Physics and Information Technology Shaanxi Normal University School of Electrical Computer and Energy Engineering Arizona State University Department of Environmental Science and Policy University of California Santa Fe Institute Department of Physics Arizona State University

Transients are fundamental to ecological systems with significant implications to management,conservation and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics are of the chaotic, predator–prey type. In the parameter regime where there is phase synchronization among all the patches, complete synchronization(i.e. synchronization in both phase and amplitude) can arise in certain pairs of patches as determined by the network symmetry—henceforth the phenomenon of ‘synchronization within synchronization.’ Distinct patterns of complete synchronization coexist but, due to intrinsic instability or noise, each pattern is a transient and there is random, intermittent switching among the patterns in the course of time evolution. The probability distribution of the transient time is found to follow an algebraic scaling law with a divergent average transient lifetime. Based on symmetry considerations, we develop a stability analysis to understand these phenomena. The general principle of symmetry can also be exploited to explain previously discovered,counterintuitive synchronization behaviors in ecological networks.

关键词： ecological networks cluster synchronization phase synchronization transient chaos network symmetry

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