Abstract
In this paper, the stochastic resonance (SR) phenomenon of four kinds of noises (the white noise, the harmonic noise, the asymmetric dichotomous noise, and the Lévy noise) in underdamped bistable systems is studied. By applying theory of stochastic differential equations to the numerical simulation of stochastic resonance problem, we simulate and analyze the system responses and pay close attention to stochastic control in the proposed systems. Then, the factors of influence to the SR are investigated by the Euler-Maruyama algorithm, Milstein algorithm, and fourth-order Runge-Kutta algorithm, respectively. The results show that the SR phenomenon can be generated in the proposed system under certain conditions by adjusting the parameters of the control effect with different noises. We also found that the type of the noise has little effect on the resonance peak of the output power spectrum density, which is not observed in conventional harmonic systems driven by multiplicative noise with only an overdamped term. Therefore, the conclusion of this paper can provide experimental basis for the further study of stochastic resonance.
Highlights
The concept of stochastic resonance (SR) was firstly proposed by Benzi et al [1] in the 1980s to explain the periodic recurrence of ice ages on Earth
We compare the system outputs driven by Gaussian white noise, harmonic noise, asymmetric dichotomous noise, and Lévy noise, which have certain guiding significance for stochastic resonance phenomenon driven by other noises, due to their wide applications
We mainly study the control effect of four kinds of noise on undamped bistable system
Summary
The concept of stochastic resonance (SR) was firstly proposed by Benzi et al [1] in the 1980s to explain the periodic recurrence of ice ages on Earth. Jia et al [5] studied SR in bistable systems driven by additive and multiplicative white noise. Guo et al [8] studied the instability probability density evolution in bistable systems driven by Gaussian noise and white noise, and obtained rich conclusions. Some literatures have begun to focus on the effects of some non-Gaussian noises on SR of bistable systems [11, 14,15,16,17]. The main goal of this paper is to focus on the control effects in an underdamped bistable system driven by four kinds of noises (the white noise, the harmonic noise, the asymmetric dichotomous noise, and the Lévy noise); we will provide the vivid numerical simulation analyses.
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