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Stochastic resonance for nonequilibrium systems.

Valerio Lucarini1

  • 1Centre for the Mathematics of Planet Earth, University of Reading, Reading RG66AX, United Kingdom; Department of Mathematics and Statistics, University of Reading, Reading RG66AX, United Kingdom; and CEN, University of Hamburg, Hamburg 20144, Germany.

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Stochastic resonance (SR) is amplified in noisy systems with two states. A new framework uses large deviation theory to describe SR in general nonequilibrium systems with periodic forcing.

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Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Complex systems

Background:

  • Stochastic resonance (SR) amplifies system response to periodic forcing in noisy environments.
  • Existing models often assume detailed balance or specific system properties.
  • Understanding SR in general nonequilibrium systems remains a challenge.

Purpose of the Study:

  • To develop a general mathematical framework for describing stochastic resonance.
  • To analyze SR in N-dimensional nonequilibrium systems with two metastable states and periodic forcing.
  • To extend the understanding of SR beyond systems obeying detailed balance.

Main Methods:

  • Utilizing large deviation theory and the theory of quasipotentials.
  • Developing a framework applicable to general drift and volatility fields.
  • Analyzing N-dimensional nonequilibrium systems with periodic forcing.

Main Results:

  • The framework recovers classical results for systems obeying detailed balance.
  • It allows expressing SR parameters and residence time statistics in terms of system fields.
  • Identified relevant forcing properties for amplifying or suppressing SR.

Conclusions:

  • The proposed framework provides a general description of stochastic resonance.
  • It offers a detailed understanding of SR in complex, periodically forced nonequilibrium systems.
  • The approach clarifies the role of forcing characteristics in modulating SR.