Stochastic Multiresonane for a Fractional Linear Oscillator with Random Viscous Damping Coefficient
Guo Xiaoying1, Zhou Yingzi1, Wang Lihua1, Wang Shixin2
1. School of Intelligent Manufacturing Panzhihua University Panzhihua 617000; 2. School of Electrical Engineering and Electronic Information Xihua University Chengdu 610039 China
Abstract：Fractional calculus has many excellent characteristics, such as dynamic memory of historical state and path dependence. Therefore, for many practical systems, fractional-order models are more suitable to use with comparison to integer-order models, especially for those dynamic processes with memory. In the study of fractional-order systems, the memory kernel function using Gamma function is a special case of that using Mittag-Leffler function. The latter is more general, especially it contains the characteristic memory time of the system, which can describe the memory effect of medium molecules on the system motion in complex and disordered heterogeneous environment. Therefore, the fractional derivative of Mittag-Leffler function can better describe the performance of the system from the two dimensions of characteristic memory time and fractal dimension. In this paper, the stochastic multiresonance for a fractional linear oscillator with random viscous damping coefficient is investigated. The memory kernel of the fractional oscillator is modeled as a Mittag-Leffler function. Based on linear system theory, applying the definition of Mittag-Leffler function and fractional derivative, the expression of the system output amplitude (SPA) is derived. Stochastic multiresonance is found on the SPA curve versus the memory time of the fractional oscillator. Stochastic resonance occurs on the curves of the SPA versus the noise flatness and the viscous damping coefficient. The SPA behaves nonmonotonically with the variety of the system frequency, of the driving frequency, as well as of the noise correlate time.
郭筱瑛, 周英姿, 王利华, 王诗心. 具有随机黏性阻尼的分数维线性振荡器中的随机多共振[J]. 电工技术学报, 2021, 36(3): 532-541.
Guo Xiaoying, Zhou Yingzi, Wang Lihua, Wang Shixin. Stochastic Multiresonane for a Fractional Linear Oscillator with Random Viscous Damping Coefficient. Transactions of China Electrotechnical Society, 2021, 36(3): 532-541.
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2021, Vol. 36 
