Stochastic Resonance of Fractional-Order System with Multiplicative Noise and Random Delay

被引：0

作者：

Zhu J. ^{[1
,2
]}

Jin W. ^{[1
]}

Guo F. ^{[3
]}

机构：

[1] School of Electrical Engineering, Southwest Jiaotong University, Chengdu

[2] School of Electrical Engineering, Chongqing University of Science and Technology, Chongqing

[3] School of Information Engineering, Southwest University of Science and Technology, Mianyang

来源：

Xinan Jiaotong Daxue Xuebao/Journal of Southwest Jiaotong University | 2021年 / 56卷 / 02期

关键词：

Fractional-order system; Multiplicative noise; Random delay; Stochastic resonance;

D O I：

10.3969/j.issn.0258-2724.20191181

中图分类号：

学科分类号：

摘要：

Time delay is a common characteristic of a dynamic system, which has been widely used in the science field. Fractional calculus has the characteristics of time memory and long-range spatial correlation, which can better describe the physical process with memory and path dependence, but rare literature have studied the phenomenon of stochastic resonance (SR) in a time-delayed fractional system. Therefore, the SR behavior for a fractional-order system with multiplicative noise and random delay is investigated. Based on linear system theory, Laplace transform and small delay approximation approach are used to derive the expression of the output amplitude gain (OAG) for the fractional-order system. It is found that the OAG is a non-monotonous function of the delay-time. The SR behavior appears on the relationship curves between the OAG and the strength and correlate rate of the multiplicative noise, between the OAG and the correlate rate of delay noise, and between the OAG and the fractional exponent and the driving frequency of the system. For relatively small multiplicative noise strength, and for the relatively small or relatively large correlation rate of multiplicative noise, the OAG decreases with the increase of the damping coefficient; while for the relatively large multiplicative noise strength, and for the medium correlation rate of multiplicative noise, the OAG increases with the damping coefficient. Copyright ©2021 JOURNAL OF SOUTHWEST JIAOTONG UNIVERSITY. All rights reserved.

引用

页码：363 / 370

页数：7

共 32 条

[1]

DONG Xiaojuan, YAN Aijun, The relationship between stochastic resonance and coherence resonance in a bi-stable system, Acta Physica Sinica, 62, 7, pp. 56-62, (2013)

[2]

JIAO Shangbin, YANG Rong, ZHANG Qing, Et al., Stochastic resonance of asymmetric bistable system with Alpha stable noise, Acta Physica Sineca, 64, 2, pp. 49-57, (2015)

[3]

GUO Feng, ZHOU Yurong, JIANG Shiqi, Et al., Stochastic resonance in a mono-stable system with multiplicative and additive noise, Journal of Physics A: Mathematical and General, 39, pp. 13861-13868, (2006)

[4]

LIU Yulei, LIANG Jun, JIAO Shangbin, Et al., Stochastic resonance of a tri-stable system with α stable noise, Chinese Journal of Physics, 55, pp. 355-366, (2017)

[5]

ZHONG Suchuan, YU Tao, ZHANG Lu, Et al., Stochastic resonance of an underdamped linear harmonic oscillator with fluctuating mass and fluctuating frequency, Acta Physica Sineca, 64, 2, pp. 28-34

[6]

FRANK T D, BEEK P J., Stationary solutions of linear stochastic delay differential equations:applications to biological systems, Physical Review E, 64, (2001)

[7]

MAJER N, SCHOLL E., Resonant control of stochastic spatiotemporal dynamics in a tunnel diode by multiple time-delayed feedback, Physical Review E, 79, (2009)

[8]

ZENG C H, SUN Y L, CHEN G X., The relaxation time of a bistable system with two different kinds of time delays, Modern Physics Letters B, 23, 18, pp. 2281-2292, (2009)

[9]

GUO Feng, ZHOU Yurong, ZHANG Yu, Stochastic resonance in a time-delayed bistable system subject to multiplicative and additive noise, Chinese Physics B, 19, 7, pp. 90-94, (2010)

[10]

HE Lifang, YANG Yulei, ZHANG Tianqi, Stochastic resonance characteristic study and bearing fault diagnosis of time-delayed feedback EVG system, Chinese Journal of Scientific Instrument, 40, 8, pp. 47-57, (2019)

← 1 2 3 4 →