Noise-induced transitions in a double-well excitable oscillator

Area of Science:

• Nonlinear Dynamics
• Stochastic Systems
• Oscillator Models

Background:

• Nonlinear dissipation in oscillator systems can lead to complex behaviors.
• Understanding stochastic dynamics is crucial for characterizing system responses to noise.
• Double-well potentials are fundamental in studying bistability and transitions.

Purpose of the Study:

• To investigate the dynamics of a double-well oscillator with nonlinear dissipation.
• To describe the self-sustained oscillation and excitable regimes.
• To analyze the effects of noise on system behavior and coherence resonance.

Main Methods:

• Numerical simulations were employed to study the stochastic dynamics.
• An electronic circuit implementation was used for experimental validation.
• Phase-space analysis of the deterministic system explained observed phenomena.

Main Results:

• Two distinct regimes were identified: self-sustained oscillations and an excitable regime.
• Coherence resonance was achieved in the excitable regime under specific noise conditions.
• Noise intensity significantly altered the probability density function, explained by phase-space structure.

Conclusions:

• The double-well oscillator model exhibits rich dynamics influenced by nonlinear dissipation and noise.
• Noise can induce or enhance oscillatory behavior (coherence resonance) in excitable systems.
• The phase-space structure provides a framework for understanding noise-induced transitions in probability density functions.