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Multistability in dynamical systems induced by weak periodic perturbations.

V N Chizhevsky1

  • 1B.I. Stepanov Institute of Physics, National Academy of Science of Belarus, 220072 Minsk, Belarus. vnc@dragon.bas-net.by

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
Summary

Weak resonant perturbations can induce multistability in nonlinear systems. The number of attractors depends on perturbation details and the system's initial state, as shown in a CO2 laser experiment.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Laser Physics

Background:

  • Nonlinear systems can exhibit complex dynamics, including routes to chaos.
  • Subharmonic resonances are known to influence system behavior.
  • Multistability, the coexistence of multiple attractors, is a key feature in some nonlinear systems.

Purpose of the Study:

  • To investigate the induction of multistability in nonlinear systems using weak resonant perturbations.
  • To determine the factors influencing the number of coexisting attractors.
  • To provide experimental and numerical evidence for the phenomenon.

Main Methods:

  • Theoretical analysis of nonlinear systems exhibiting period-doubling or isolated subharmonic branches.
  • Numerical simulations to model system dynamics under perturbation.

Related Experiment Videos

  • Experimental validation using a loss-modulated carbon dioxide (CO2) laser.

    • Main Results:

    • Weak resonant perturbations at subharmonic frequencies can induce multistability.
    • The number of induced attractors is sensitive to perturbation frequency, amplitude, and phase.
    • The initial dynamical state of the system also affects the outcome.
    • Experimental and numerical results align, confirming the findings.

    Conclusions:

    • Subharmonic resonant perturbations offer a method to control and induce multistability in nonlinear systems.
    • Understanding these dependencies is crucial for predicting and manipulating complex system behavior.
    • The findings have implications for systems ranging from lasers to other nonlinear oscillators.