Stochastic resonance and superharmonic resonance of a noisy confined overdamped bistable system

Abstract Most previous studies on stochastic resonance (SR) have focused on models without boundaries. However, the dynamics of the confined systems are affected by space limitations, which exert unique effects on the reaction, diffusion, and SR behavior of systems. Some subsequent studies have discussed the SR-like phenomena in the 2D confined spaces in the presence of uneven boundaries. However, few reports have been published the response and SR of Brownian particle movement in a 1D space restricted by constant boundaries. In this paper, we considered an overdamped bistable system excited by a periodic driving force and an additive Gaussian white noise in the presence of constant restricted boundaries, and studied the response and SR phenomena of this confined system from the perspectives of limit cycle and potential function. The presence of the baffles changes the shape of the system potential function and limit cycles, thereby changing the dynamic properties of the system. Therefore, the SR of the confined system also undergoes significant changes compared with the original unconfined bistable system. It pointed out a criterion for SR of the confined overdamped bistable system on the basis of the relative position of limit cycles of the deterministic confined system and baffles.