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Related Experiment Videos

Stochastic resonance in the brusselator model

Osipov1, Ponizovskaya

  • 1Department of Theoretical Physics, Russian Science Center "ORION," Plekhanova Street 2/46, 111123 Moscow, Russia.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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In dynamical systems, small noise can amplify into large bursting oscillations near a Hopf bifurcation. Periodic signals can then control these oscillations, creating either quasiperiodic or quasiharmonic behaviors.

Area of Science:

  • Nonlinear dynamics
  • Chemical kinetics
  • Stochastic processes

Background:

  • The Brusselator model is a well-known example of a system exhibiting complex dynamics.
  • Hopf bifurcations are critical points where oscillatory behavior emerges in dynamical systems.
  • Stochastic resonance is a phenomenon where noise can enhance signal detection.

Purpose of the Study:

  • To investigate the conversion of small noise into large amplitude oscillations in a simple dynamical system.
  • To explore the effect of external periodic signals on these noise-induced oscillations.
  • To understand the role of signal form in determining the resulting oscillatory behavior.

Main Methods:

  • Utilized the Brusselator model, a set of ordinary differential equations.

Related Experiment Videos

  • Analyzed system behavior in the vicinity of a Hopf bifurcation.
  • Introduced controlled levels of noise and periodic signals to the system.

    • Main Results:

    • Demonstrated that small noise can be amplified into large-amplitude stochastic spikewise oscillations (bursting noises).
    • Showed that small periodic signals can transform these stochastic oscillations into quasiperiodic large-amplitude spikewise oscillations.
    • Observed that the signal form determines whether quasiharmonic small-amplitude oscillations emerge.

    Conclusions:

    • Noise-induced oscillations can be significant in simple dynamical systems near bifurcations.
    • External signals can effectively control and shape these stochastic oscillations.
    • The interplay between noise, signal characteristics, and system dynamics is crucial for emergent behaviors.