Explosive synchronization caused by optimizing synchrony of coupled phase oscillators on complex networks

Wei Chen (), Shengfeng Wang, Yueheng Lan, Weiqing Liu and Jinghua Xiao ()
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Wei Chen: Beijing University of Posts and Telecommunications
Shengfeng Wang: Beijing University of Posts and Telecommunications
Yueheng Lan: Beijing University of Posts and Telecommunications
Weiqing Liu: Jiangxi University of Science and Technology
Jinghua Xiao: Beijing University of Posts and Telecommunications

The European Physical Journal B: Condensed Matter and Complex Systems, 2021, vol. 94, issue 10, 1-10

Abstract: Abstract We optimize synchrony in networks of heterogeneous phase oscillators. By analyzing the eigenvalues of the Jacobian matrix at full synchronization, two structure indicators related to the critical coupling strength are constructed. When the network structure is fixed, the current scheme of optimization on the frequency picking and allocation converts the synchronization from a second-order continuous to a first-order discontinuous phase transition. When the frequency distribution is deterministic and uniform, the obtained best network structure has a critical coupling strength that approaches the theoretical minimum value. It is found that the requirement for explosive synchronization is consistent with that for optimizing synchrony, which requires that the frequency difference between connected nodes be large, and the distance from the node to the average frequency is proportional to the node degree. The connection between optimization and explosive synchronization deepens our understanding of the latter and provides an effective way of control. Graphic abstract

Date: 2021
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DOI: 10.1140/epjb/s10051-021-00201-z

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