Abstract
So far the analysis of stochastic and vibrational resonances has been focused in monostable and bistable systems. It is important to investigate also the resonance dynamics in multistable systems, particularly, in spatially periodic potential systems. This is because there are many nonlinear systems with multistable states and moreover such studies might help us to know how does multistable states affect resonance dynamics and explore the role of them on the characteristics of a resonance. It has been shown that [1] the noise-induced resonant behaviour exhibited in a pendulum (its potential is spatially periodic) is not the stochastic resonance associated with the hopping between the wells. However, the observed resonance is a noise enhanced resonance due to the intra-well motion. In the case of large damping and weak periodic force, the distribution of escape time displayed a series of stochastic resonance-like peaks with noise intensity [2]. Such a character is not observed with a diffusion coefficient. Nicolis [3] investigated the stochastic resonance in a potential with an arbitrary number of minima and maxima. Employing a linear response theory, an optimal number of minima and maxima giving a maximum response is obtained. Saika et al. [4] have shown the occurrence of stochastic resonance in the pendulum system with the driving frequency close to the natural frequency and have used an input energy and a hysteresis loop area as its characteristic measures.
Published Version
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