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Memory-dependent noise-induced resonance and diffusion in non-Markovian systems.

S S Melnyk1, O V Usatenko1, V A Yampol'skii2

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This study analyzes non-Markovian systems with nonlocal memory, identifying boundaries between stationary and nonstationary dynamics. It reveals two boundary types: diffusion with memory and noise-induced resonance without external forces.

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Area of Science:

  • Statistical Physics
  • Non-Markovian Dynamics
  • Complex Systems

Background:

  • Non-Markovian systems exhibit memory effects, deviating from standard Markovian assumptions.
  • The Mori-Zwanzig equation is a key tool for describing the dynamics of such systems.
  • Understanding the transition between stationary and nonstationary behavior is crucial for characterizing system stability.

Purpose of the Study:

  • To investigate random processes with nonlocal memory.
  • To derive solutions for the Mori-Zwanzig equation in non-Markovian systems.
  • To analyze system dynamics based on local (ν) and nonlocal (μ₀) memory amplitudes and identify phase transition boundaries.

Main Methods:

  • Solving the Mori-Zwanzig equation for non-Markovian systems.
  • Analyzing system dynamics in the (ν, μ₀) parameter space.
  • Deriving general equations for boundaries between stationary and nonstationary regimes.
  • Examining specific nonlocal memory functions.

Main Results:

  • Identified two distinct types of boundaries separating stationary and nonstationary dynamics.
  • Boundary type 1: Characterized by diffusion with memory.
  • Boundary type 2: Exhibits noise-induced resonance, occurring without external periodic forces due to noise spectrum frequencies matching system self-frequencies.

Conclusions:

  • The study elucidates the complex dynamics of non-Markovian systems with nonlocal memory.
  • Noise-induced resonance in these systems is a significant finding, driven by internal noise characteristics.
  • The identified boundaries provide critical insights into system stability and behavior transitions.