Complexity in Hamiltonian-driven dissipative chaotic dynamical systems

Y C Lai, C Grebogi, Ying-Cheng Lai

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The existence of symmetry in chaotic dynamical systems often leads to one or several low-dimensional invariant subspaces in the phase space. We demonstrate that complex behaviors can arise when the dynamics in the invariant subspace is Hamiltonian but the full system is dissipative. In particular, an infinite number of distinct attractors can coexist. These attractors can be quasiperiodic, strange nonchaotic, and chaotic with different positive Lyapunov exponents. Finite perturbations in initial conditions or parameters can lead to a change from nonchaotic attractors to chaotic attractors. However, arbitrarily small perturbations can lead to dynamically distinct chaotic attractors. This work demonstrates that the interplay between conservative and dissipative dynamics can give rise to rich complexity even in physical systems with a few degrees of freedom.

Original languageEnglish
Pages (from-to)4667-4675
Number of pages9
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume54
Issue number5
Publication statusPublished - Nov 1996

Keywords

  • STRANGE NONCHAOTIC ATTRACTORS
  • AREA-PRESERVING MAPS
  • BASIN BOUNDARIES
  • RIDDLED BASINS
  • TRANSPORT
  • BIRTH

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