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Non-Markovian stochastic resonance.

Igor Goychuk1, Peter Hänggi

  • 1Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany.

Physical Review Letters
|August 26, 2003
PubMed
Summary
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We present a new theory for non-Markovian stochastic resonance (SR) in two-state systems. This theory reveals that genuine non-Markovian SR shows unique behavior at low frequencies, with suppressed signal-to-noise ratio (SNR) compared to Markovian SR.

Area of Science:

  • Theoretical physics
  • Non-linear dynamics
  • Biophysics

Background:

  • Stochastic resonance (SR) is a phenomenon where a periodic signal is enhanced by noise.
  • Existing SR theories primarily focus on Markovian processes, limiting their applicability to systems with memory effects.

Purpose of the Study:

  • To develop a phenomenological linear response theory for non-Markovian stochastic resonance (SR).
  • To investigate the characteristic quantifiers of SR, namely spectral power amplification (SPA) and signal-to-noise ratio (SNR), in non-Markovian systems.
  • To elucidate the theory using a model of potassium ion channel gating dynamics.

Main Methods:

  • Derivation of a non-Markov regression theorem.
  • Evaluation of SR quantifiers (SPA and SNR) for stationary two-state renewal processes.

Related Experiment Videos

  • Application of the theory to a potassium ion channel with fractal gating dynamics.

    • Main Results:

    • The developed theory captures genuine non-Markovian SR effects.
    • A distinctive dependence of SPA and SNR on small (adiabatic) driving frequencies is observed.
    • The adiabatic SNR is found to be strongly suppressed compared to its Markovian counterpart.

    Conclusions:

    • The study provides a theoretical framework for understanding non-Markovian SR.
    • Non-Markovian dynamics introduce unique features in SR phenomena, particularly at low frequencies.
    • The findings are relevant for understanding ion channel gating and other biological processes with memory.