中国物理B ›› 2013, Vol. 22 ›› Issue (8): 80202-080202.doi: 10.1088/1674-1056/22/8/080202

• GENERAL • 上一篇    下一篇

The dynamics of a symmetric coupling of three modified quadratic maps

Paulo C. Rech   

  1. Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil
  • 收稿日期:2012-10-22 修回日期:2013-01-26 出版日期:2013-06-27 发布日期:2013-06-27
  • 基金资助:
    Project supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq, Brazil.

The dynamics of a symmetric coupling of three modified quadratic maps

Paulo C. Rech   

  1. Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil
  • Received:2012-10-22 Revised:2013-01-26 Online:2013-06-27 Published:2013-06-27
  • Contact: Paulo C. Rech E-mail:dfi2pcr@joinville.udesc.br
  • Supported by:
    Project supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq, Brazil.

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摘要： We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we investigate the emergence of quasiperiodic states arising from Naimark-Sacker bifurcations of stable period-1, period-2, and period-3 orbits. We also investigate the multistability in the same coupling. Lyapunov exponents, parameter planes, phase space portraits, and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states, from quasiperiodic to mode-locked states and to chaotic states, and from chaotic to hyperchaotic states.

关键词: Naimark-Sacker bifurcation, quasiperiodicity, chaos, hyperchaos

Abstract: We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we investigate the emergence of quasiperiodic states arising from Naimark-Sacker bifurcations of stable period-1, period-2, and period-3 orbits. We also investigate the multistability in the same coupling. Lyapunov exponents, parameter planes, phase space portraits, and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states, from quasiperiodic to mode-locked states and to chaotic states, and from chaotic to hyperchaotic states.

Key words: Naimark-Sacker bifurcation, quasiperiodicity, chaos, hyperchaos

中图分类号:  (Integral equations)

  • 02.30.Rz
05.45.-a (Nonlinear dynamics and chaos)