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Gain in stochastic resonance: precise numerics versus linear response theory beyond the two-mode approximation
Jesús Casado-Pascual1, Claus Denk, José Gómez-Ordóñez
1Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, Spain.
Summary
Stochastic resonance (SR) in bistable systems shows that gain can exceed unity, challenging linear response theory (LRT) predictions. Numerical simulations reveal deviations from LRT, especially in nonlinear regimes with specific input signals.
Area of Science:
- Nonlinear Dynamics
- Statistical Physics
- Stochastic Processes
Background:
- Stochastic resonance (SR) is a phenomenon where a nonlinear system exhibits enhanced response to a weak periodic signal due to the presence of noise.
- Linear response theory (LRT) is often used to analyze SR, typically employing approximations like the two-mode scheme.
- Understanding the quantifiers of SR, such as correlation function, signal-to-noise ratio (SNR), and gain, is crucial for characterizing system behavior.
Purpose of the Study:
- To investigate the correlation function, SNR, and gain in a bistable system under periodic driving and noise, extending beyond standard LRT approximations.
- To analytically and numerically assess the validity of LRT predictions for SR quantifiers.
- To explore conditions under which the gain can deviate from LRT predictions, particularly exceeding unity.
Main Methods:
- Evaluation of SR quantifiers using linear response theory (LRT) beyond the two-mode approximation.
- Implementation of an efficient algorithm to numerically integrate the driven Langevin equation.
- Comparison of LRT predictions with numerical solutions of the Langevin equation across a wide parameter range.
Main Results:
- Analytical demonstration within extended LRT that gain does not exceed unity.
- Numerical results show that for subthreshold driving, correlation function and SNR can deviate substantially from LRT predictions.
- The gain can exceed unity in the strongly nonlinear regime with weak noise and slow multifrequency input signals, contradicting standard LRT.
Conclusions:
- Standard LRT provides an incomplete description of SR, especially in strongly nonlinear regimes.
- Numerical simulations are essential for accurately characterizing SR quantifiers beyond simplified theoretical frameworks.
- The phenomenon of gain exceeding unity is possible under specific conditions of weak noise and complex input signals.