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Phase velocity and phase diffusion in periodically driven discrete-state systems.

T Prager1, L Schimansky-Geier

  • 1Institute of Physics, Humboldt-University of Berlin, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
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We developed a theory for periodically driven stochastic systems with two states. This theory reveals bona fide resonance and stochastic synchronization with periodic driving in both Markovian and non-Markovian models.

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • Stochastic systems with discrete states are fundamental in various scientific fields.
  • Understanding their response to periodic driving is crucial for analyzing phenomena like resonance and synchronization.

Purpose of the Study:

  • To develop a theoretical framework for calculating effective phase diffusion and mean phase velocity in periodically driven two-state stochastic models.
  • To investigate stochastic synchronization and resonance phenomena in both Markovian and non-Markovian systems.

Main Methods:

  • Analytical derivation of expressions for mean phase velocity, effective phase diffusion coefficient, and Péclet number.
  • Application of the developed theory to a dichotomically driven Markovian two-state system.

Related Experiment Videos

  • Extension of the theory to a non-Markovian two-state system modeling excitable systems.

    • Main Results:

    • Explicit analytical expressions for key parameters were obtained for the Markovian system.
    • The Péclet number was identified as a measure of phase-coherence and forced synchronization, exhibiting resonance.
    • The theory accurately predicted stochastic synchronization in a non-Markovian excitable system, consistent with simulations.

    Conclusions:

    • The developed theory provides a robust method for analyzing periodically driven stochastic systems.
    • Stochastic synchronization and bona fide resonance are key features of these systems under periodic forcing.
    • The findings are applicable to diverse systems, including excitable models like the FitzHugh-Nagumo system.