Stochastic resonance in periodically driven bistable systems subjected to anomalous diffusion

Abstract

The occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with emphasis on the analytical formulation of the problem as well as a possible analytical derivation of key quantifiers of stochastic resonance. The nonlinear Fokker-Planck equation describing the system dynamics, together with the corresponding Ito-Langevin equation, are formulated. In the linear-response regime analytical expressions of the spectral amplification, of the signal-to-noise ratio and of the hysteresis loop area are derived as quantifiers of stochastic resonance. These quantifiers are found to be strongly dependent on the parameters controlling the type of diffusion, in particular the peak characterizing the signal-to-noise ratio occurs only in close ranges of parameters. Results introduce the relevant information that taking into consideration the interactions of anomalous diffusive systems with a periodic signal, can provide a better understanding of the physics of stochastic resonance in bistable systems driven by periodic forces.

arXiv comment10 pages, 7 figures

References in corpus (8)

• Anomalous diffusion in the presence of external forces: exact time-dependent solutions and entropy
• From Diffusion to Anomalous Diffusion: A Century after Einstein's Brownian Motion
• Divergent Signal-to-Noise Ratio and Stochastic Resonance in Monostable Systems
• From subdiffusion to superdiffusion of particles on solid surfaces
• Escape time in anomalous diffusive media
• Kramers escape of a self-propelled particle
• Stochastic resonance in bistable confining potentials. On the role of confinement
• Anomalous Diffusion and Stress Relaxation in Surfactant Micelles