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Bistable chaos without symmetry in generalized synchronization.

Shuguang Guan1, C-H Lai, G W Wei

  • 1Temasek Laboratories, National University of Singapore, 5 Sports Drive 2, 117508 Singapore.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
Summary

This study reveals bistable chaos in generalized synchronization (GS) for coupled chaotic systems, even without symmetry. It explores crisis bifurcations and analyzes fractal basin boundaries, offering new insights into complex dynamical systems.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Multistable chaos is commonly observed in symmetric dynamical systems.
  • Generalized synchronization (GS) typically occurs in systems exhibiting symmetry.
  • Bistable chaos in GS, characterized by two coexisting synchronized chaotic attractors, is rare, especially in asymmetric systems.

Purpose of the Study:

  • To demonstrate and analyze bistable chaos in generalized synchronization (GS) within coupled chaotic systems, specifically focusing on a rare instance in asymmetric configurations.
  • To identify and characterize different types of bistable chaos and the bifurcations leading to them.
  • To investigate the basins of attraction for bistable attractors and their properties.

Main Methods:

  • Investigating coupled chaotic systems with tunable coupling to induce symmetric or asymmetric configurations.

Related Experiment Videos

  • Analyzing crisis bifurcations to understand the onset of bistability.
  • Exploring parameter and initial condition spaces to study the basins of attraction.
  • Characterizing fractal basin boundaries and riddled basins using the uncertainty exponent.

    • Main Results:

    • Bistable chaos in GS was observed in coupled chaotic systems, both with and without symmetry.
    • Three distinct types of bistable chaos were identified.
    • Crisis bifurcations were found to be responsible for the emergence of bistability.
    • Analysis revealed fractal basin boundaries and riddled basins associated with the bistable attractors.

    Conclusions:

    • Bistable chaos in GS can occur in coupled chaotic systems irrespective of symmetry, challenging previous assumptions.
    • The study provides a comprehensive analysis of the mechanisms, types, and basin structures of bistable chaos in GS.
    • Findings contribute to a deeper understanding of complex dynamics and synchronization phenomena in nonlinear systems.