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

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.