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Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Complex systems

Background:

  • Noise significantly impacts nonlinear dynamical systems.
  • Single-well potentials of the form |x|^n are fundamental in modeling various physical phenomena.
  • Understanding noise-induced transitions is crucial for characterizing system behavior.

Purpose of the Study:

  • To investigate the conditions under which Ornstein-Uhlenbeck noise induces bimodality in static, single-well, power-law potentials.
  • To analyze the transition from unimodal to bimodal stationary states as a function of the potential exponent (n).
  • To explore the influence of a harmonic potential addition on the system's dynamics.

Main Methods:

  • Numerical simulations of the noise-perturbed dynamical system.
  • Analytical estimates using the unified colored-noise approximation.
  • Analysis of potential landscapes and stationary state distributions.

Main Results:

  • Identified the critical exponent threshold (n>2) for the emergence of bimodality.
  • Demonstrated that Ornstein-Uhlenbeck noise can drive systems from unimodal to bimodal states.
  • Showcased the constructive or destructive role of harmonic potential additions.

Conclusions:

  • The exponent of the power-law potential is a key factor determining the noise-induced bimodality.
  • The unified colored-noise approximation provides reliable estimates for system behavior.
  • Harmonic potentials can either stabilize or destabilize the system, modulating the noise effects.