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Stochastic resonance in a trapping overdamped monostable system.
N V Agudov1, A V Krichigin, D Valenti
1Radiophysics Faculty, Nizhniy Novgorod State University, 23 Gagarin Avenue, 603950 Nizhniy Novgorod, Russia. agudov@rf.unn.ru
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
Stochastic resonance in overdamped systems is analyzed. The signal-to-noise ratio non-monotonically depends on noise intensity, while signal power amplification monotonically increases with noise.
Area of Science:
- Physics
- Nonlinear Dynamics
- Statistical Mechanics
Background:
- Stochastic resonance (SR) is a phenomenon where a non-linear system exhibits enhanced response to a weak periodic signal due to the presence of noise.
- Overdamped monostable systems are fundamental models for studying SR, particularly those with piecewise potentials.
- Understanding the interplay between noise, potential landscape, and system response is crucial for various applications.
Purpose of the Study:
- To analyze the response of a trapping overdamped monostable system subjected to harmonic perturbation within the framework of stochastic resonance.
- To derive analytical expressions for key performance metrics: signal-to-noise ratio (SNR) and signal power amplification (SPA).
- To investigate the dependence of SNR and SPA on noise intensity.
Main Methods:
- Modeling the system dynamics using a Brownian particle in a piecewise linear potential subjected to white Gaussian noise.
- Applying linear-response theory to derive analytical expressions for SNR and SPA.
- Utilizing the Laplace transform technique for mathematical analysis.
- Comparing theoretical predictions with results from numerical simulations.
Main Results:
- The signal-to-noise ratio (SNR) was found to be a nonmonotonic function of the noise intensity, exhibiting a characteristic peak.
- The signal power amplification (SPA) demonstrated a monotonic increase with increasing noise intensity.
- Analytical results were validated through numerical simulations, confirming the theoretical predictions.
Conclusions:
- The study provides a comprehensive analytical treatment of stochastic resonance in a specific class of overdamped systems.
- The distinct behaviors of SNR (nonmonotonic) and SPA (monotonic) with respect to noise intensity offer valuable insights into system optimization.
- The findings contribute to the fundamental understanding of noise-induced phenomena in nonlinear systems and their potential applications.
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