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Multistability and the control of complexity.

Ulrike Feudel1, Celso Grebogi

  • 1Institut fur Physik, Universitat Potsdam, PF 601553, D-14415 Potsdam, Germany.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
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Multistable systems, common in nonlinear dynamics, primarily exhibit periodic attractors, making chaotic attractors rare. Controlling complexity allows for stabilizing or destabilizing these coexisting states.

Area of Science:

  • Nonlinear Dynamics
  • Complex Systems Theory
  • Chaos Theory

Background:

  • Multistability is a phenomenon where dynamical systems exhibit multiple coexisting stable states or attractors.
  • Understanding the nature and prevalence of different attractor types in multistable systems is crucial for characterizing their behavior.
  • Complex systems often display multistability, necessitating methods for their analysis and control.

Purpose of the Study:

  • To elucidate the origins and characteristics of multistability in nonlinear dynamical systems.
  • To investigate the typical attractor properties within multistable systems, specifically the rarity of chaotic attractors.
  • To introduce and demonstrate a novel approach for controlling the complexity of multistable systems.

Main Methods:

Related Experiment Videos

  • Analysis of nonlinear dynamical systems exhibiting multistability.
  • Characterization of attractor types (periodic vs. chaotic) within these systems.
  • Development and application of 'controlling complexity' methods for state manipulation.

    • Main Results:

    • Demonstrated that most attractors in multistable systems are periodic.
    • Established that chaotic attractors are infrequent in such systems.
    • Showcased the ability to stabilize or destabilize specific coexisting states using the 'controlling complexity' approach.

    Conclusions:

    • Multistable systems predominantly feature periodic dynamics, with chaos being an exception.
    • The 'controlling complexity' framework offers a new paradigm for manipulating dynamical systems, distinct from traditional chaos control.
    • This approach provides precise control over the coexisting states within complex, multistable systems.