Response and Bifurcation of Fractional Duffing Oscillator under Combined Recycling Noise and Time-Delayed Feedback Control

Q3 Multidisciplinary
Fang WANG, Jiangang ZHANG
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引用次数: 0

Abstract

Response and bifurcation of fractional Duffing oscillator under recycling noise and time-delayed feedback control are investigated. Firstly, based on the principle of the minimum mean square error and small time-delayed approximation and linearize the cubic stiffness term, the fractional derivative is equivalent to a linear combination of damping and restoring forces, and the original system is simplified into an equivalent integer order system. Secondly, the Itô differential equations and one-dimensional Markov process are obtained according to stochastic averaging method, and the stochastic stability and stochastic bifurcation of the system are analyzed. Lastly, through joint probability density function diagram and the stationary probability density function diagram, the stochastic bifurcation behavior of system under the different time-delay, fractional order and noise intensity are discussed respectively, the validity of the theory and the occurrence of bifurcation phenomenon are verified.
循环噪声与时滞反馈联合控制下分数阶Duffing振荡器的响应与分岔
研究了分数阶Duffing振荡器在循环噪声和时滞反馈控制下的响应和分岔问题。首先,基于最小均方误差和小时滞逼近原理,对三次刚度项进行线性化处理,将分数阶导数等效为阻尼力和恢复力的线性组合,将原系统简化为等效的整数阶系统;其次,根据随机平均法得到了系统的Itô微分方程和一维马尔可夫过程,并对系统的随机稳定性和随机分岔进行了分析;最后,通过联合概率密度函数图和平稳概率密度函数图,分别讨论了系统在不同时滞、分数阶和噪声强度下的随机分岔行为,验证了理论的有效性和分岔现象的发生。
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来源期刊
Wuhan University Journal of Natural Sciences
Wuhan University Journal of Natural Sciences Multidisciplinary-Multidisciplinary
CiteScore
0.40
自引率
0.00%
发文量
2485
期刊介绍: Wuhan University Journal of Natural Sciences aims to promote rapid communication and exchange between the World and Wuhan University, as well as other Chinese universities and academic institutions. It mainly reflects the latest advances being made in many disciplines of scientific research in Chinese universities and academic institutions. The journal also publishes papers presented at conferences in China and abroad. The multi-disciplinary nature of Wuhan University Journal of Natural Sciences is apparent in the wide range of articles from leading Chinese scholars. This journal also aims to introduce Chinese academic achievements to the world community, by demonstrating the significance of Chinese scientific investigations.
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