Stochastic resonance across bifurcation cascades

Area of Science:

• Nonlinear dynamics
• Statistical physics
• Signal processing

Background:

• Stochastic resonance (SR) typically studies systems with fixed states.
• Parameter variations can alter system dynamics, affecting signal processing capabilities.

Purpose of the Study:

• To extend the classical stochastic resonance framework to include parameter variations.
• To analyze transitions between different dynamical regimes (unique stable state, bistability, multistability).
• To derive analytical expressions for system response and identify optimal conditions.

Main Methods:

• Analysis of stochastic differential equations with varying parameters.
• Bifurcation analysis to identify transitions between states.
• Derivation of analytic expressions for response amplitude and phase.

Main Results:

• Developed a generalized framework for stochastic resonance under parameter variations.
• Characterized transitions across various singularities, including unique stable state, bistability, and multistability.
• Obtained analytic expressions for response amplitude and phase.
• Derived conditions for optimal stochastic resonance based on bifurcation parameter, driving frequency, and noise strength.

Conclusions:

• Parameter variations significantly impact stochastic resonance phenomena.
• The derived framework provides a quantitative understanding of optimal signal processing in systems with changing dynamics.
• This work offers insights into designing systems that leverage stochastic resonance for enhanced performance.