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Dynamics and synchronization of a complex-valued star network

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Abstract

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 symmetry-breaking phenomenon.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Jinan, Jinan, 250022, China

    Lin Chai, Jian Liu & Xiu Zhao

  2. Department of Electrical Engineering, City University of Hong Kong, Hong Kong, China

    GuanRong Chen

Authors
  1. Lin Chai
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  2. Jian Liu
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  3. GuanRong Chen
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  4. Xiu Zhao
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Corresponding author

Correspondence to Jian Liu.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 61773010).

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Chai, L., Liu, J., Chen, G. et al. Dynamics and synchronization of a complex-valued star network. Sci. China Technol. Sci. 64, 2729–2743 (2021). https://doi.org/10.1007/s11431-021-1929-8

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  • DOI: https://doi.org/10.1007/s11431-021-1929-8

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