Complex dynamical networks have emerged as powerful tools for studying the characteristics and evolutions of various real-world social and engineering networks,such as multi-agent systems,power grids,biological networ...Complex dynamical networks have emerged as powerful tools for studying the characteristics and evolutions of various real-world social and engineering networks,such as multi-agent systems,power grids,biological networks,and epidemic spreading.The study of complex dynamical networks is crucial for understanding complex systems and provides a solid theoretical foundation for network science and engineering.展开更多
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 couple...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.展开更多
文摘Complex dynamical networks have emerged as powerful tools for studying the characteristics and evolutions of various real-world social and engineering networks,such as multi-agent systems,power grids,biological networks,and epidemic spreading.The study of complex dynamical networks is crucial for understanding complex systems and provides a solid theoretical foundation for network science and engineering.
基金Project supported by the National Natural Science Foundation of China(Nos.21602055,21302048)the Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province(No.2012-318)the Construct Program of the Key Discipline in Hunan Province~~
基金the National Natural Science Foundation of China(Grant No.61773010)。
文摘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.
