Double stochastic energetic resonance of underdamped two-scale bistable system

Abstract Multistable structures have abundant nonlinear characteristics, a multi-level system with large-scale and small-scale bistable structures is constructed, and its dynamic characteristic is discussed. Based on the complete Langevin equation with an inertial term and a variable damping term, the relationship between the Kramers escape rate and the damping coefficient is deduced and the approximate analytical expression of the output response in the underdamped state is established. From the view of the energy, the mechanism of double resonance and resonance effect enhancement induced by damping is further revealed with the energy dissipation caused by damping as the core. The physical quantity work is introduced to measure the strength of the resonance effect. The results of theoretical analysis and numerical simulation indicate that as the damping coefficient decreases into the underdamping or even the weak damping scope, the double stochastic resonance phenomenon induced by noise still exists. The strongest resonance effect can be obtained with the optimal damping value.