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Mar 9, 2021

Synchronization dynamics in coupled oscillator networks: heterogeneity effect

Zhigang Zheng, Institute of Systems Science, National Huaqiao University



Synchronization of networks of coupled oscillators has long been an important topic in relating a lot of issues. Network structure leads to nontrivial phase transitions, such as explosive synchronization and cluster synchronization. Besides the usual diversity in natural frequencies of oscillators, heterogeneity in the coupling strength (i.e., weighted networks) is also an important characteristic in many real systems and induces the emergence of various coherent states in the route to synchronization.
In this talk we consider the influence of natural-frequency heterogeneities on the coupling and develop the order parameter analysis and the self-consistency approach to get the low-dimensional behaviors of coupled phase oscillators. Rigorous stability for the phase-locked state is analyzed from different levels. We give general conditions for the stability of the phase-locked state based on the properties of eigen spectrum and the associated eigenvectors. We reveal universal routes to synchronization from the incoherent state to the oscillatory state and then to the phase-locked state. These findings are significant in revealing the universality and the diversity of synchronization transitions of networks of oscillators with heterogeneous couplings.


Dr. Zhigang Zheng is currently the distinguished professor and the director of Institute of Systems Science at National Huaqiao University. He is also a recipient of the Minjiang Distinguished Professor Plan in 2015, the One-hundred Talents in Fujian in 2017. He acts as the member of Editorial Board of Scientific Reports, Chaos, JAND, CPB and other journals. Zheng received the Ph.D. degree in physics from Beijing Normal University, Beijing, China, in 1998. He was the dean and the Professor of physics at Beijing Normal University during 2001-2015, and a Visiting professor with California Institute of Technology, Pasadena, CA, USA during 2001-2002. Zheng’s research interests cover nonlinear dynamics, synchronization, complex systems and complex networks, and non-equilibrium statistical mechanics. He has published 5 monographs and over 200 scientific papers in these fields.


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