Stochastic resonance in one-dimensional diffusion with one reflecting and one absorbing end point

Area of Science:

• Statistical Physics
• Nonlinear Dynamics
• Diffusion Processes

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.
• Diffusion on a bounded segment with absorbing and reflecting endpoints is a common model in various physical and biological systems.

Purpose of the Study:

• To analyze the non-monotonic dependence of mean-free-passage time on signal frequency in a diffusion process exhibiting stochastic resonance.
• To determine the conditions under which stochastic resonance occurs for periodic and random telegraph signals in a confined diffusion system.

Main Methods:

• Mathematical analysis of the mean-free-passage time for diffusion on a segment with one absorbing and one reflecting endpoint.
• Investigation of stochastic resonance under periodic and random telegraph signal forcing.

Main Results:

• Stochastic resonance was found to exist only for restricted parameter values when using a periodic signal.
• Stochastic resonance was observed to consistently exist when the periodic signal was replaced by a random telegraph signal.
• Detailed analysis of the stochastic resonance phenomenon with random signals was performed.

Conclusions:

• The presence and characteristics of stochastic resonance are highly dependent on the nature of the external signal (periodic vs. random).
• Random telegraph signals offer a more robust condition for observing stochastic resonance in this diffusion model compared to periodic signals.