Dynamics and synchronization of a complex-valued star network  

作　　者：CHAI Lin LIU Jian CHEN GuanRong ZHAO Xiu 

机构地区：[1]School of Mathematical Sciences,University of Jinan,Jinan 250022,China [2]Department of Electrical Engineering,City University of Hong Kong,Hong Kong,China

出　　处：《Science China(Technological Sciences)》2021年第12期2729-2743,共15页中国科学（技术科学英文版）

基　　金：the National Natural Science Foundation of China(Grant No.61773010)。

摘　　要：Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of coupled complex-valued van der Pol oscillators is proposed to reveal the mechanism of star coupling.By the aid of bifurcation diagram,Lyapunov exponent spectrum and phase portrait in this study,chaos,hyper-chaos,and multi-existing chaotic attractors are observed from the star network,although there are only periodic states in a complex-valued van der Pol oscillator.Complexity versus coupling strength and nonlinear coefficient shows that the bigger the network size,the larger the parameter range within the chaotic(hyper-chaotic)region.It is revealed that the chaotic bifurcation path is highly robust against the size variation of the star network,and it always evolves to chaos directly from period-1 and quasi-periodic states,respectively.Moreover,the coexistence of chaotic phase synchronization and complete synchronization among the peripherals is also found from the star network,which is a symmetrybreaking phenomenon.

关 键 词：star network chaotic phase synchronization complex-valued van der Pol oscillator SYMMETRY-BREAKING 

分 类 号：O157.5[理学—数学] TN752[理学—基础数学]