Study on the mean first-passage time and stochastic resonance of a multi-stable system with colored correlated noises

The mean first-passage time (MFPT) and the weak signal detection method of stochastic resonance (SR) on multi-stable nonlinear system under color correlated noise are studied. Using the uniform color noise approximation method, the Fokker-Planck equation of the system is obtained, and the steady-state probability density function of the multi-stable system driven by the multiplicative noise and additive noise is derived. On the basis of this, the formula of MFPT is derived, and the influence of parameters on the MFPT is analyzed. The problem of weak signal detection under color noise background is studied based on multi-stable SR. The results of simulation and experiment show that the method can effectively extract the frequency feature of weak signal in the background of color noise.

Automated summary

This study focused on the mean first-passage time (MFPT) and weak signal detection method of stochastic resonance (SR) on a multi-stable nonlinear system under color correlated noise. The Fokker-Planck equation of the system and the steady-state probability density function of the multi-stable system were derived, leading to the analysis of the MFPT and its parameter influences. Furthermore, the weak signal detection problem under color noise background was explored, demonstrating the effective extraction of weak signal frequency features using the proposed method.