Bifurcation Analysis of a Class Fractional-Oder Nonlinear Chua’s Circuit System
Zhe Zhang*, Toshimitsu Ushio**, Jing Zhang*, Can Ding*, and Feng Liu***
*College of Electrical and Information Engineering, Hunan University
Lushan Road, Yuelu District, Changsha, Hunan 410082, China
**Graduate School of Engineering Science, Osaka University
1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
***School of Automation, China University of Geosciences (Wuhan)
388 Lumo Road, Hongshan District, Wuhan 430074, China
In recent years, with the rapid development of science and technology, dynamic characterization and control of the research circuit system has become not only theoretical but also practical consideration in academic research and practical engineering applications. Therefore, the complex behavior of a research circuit system has become a hot spot in the theoretical field. This thesis is aimed toward the stability criterion and bifurcation of the fractional-order Chua’s circuit system. Despite numerous studies relating to the Chua’s system, most of them focus on its sum of delays. Different from traditional bifurcation analysis of Chua’s circuit system, the parameters are chosen as the bifurcation parameters in this paper such that the stability and bifurcation of the fractional-order Chua’s system is analyzed from a new angle. Then, the conditions of the existence for Hopf bifurcations are achieved by analyzing its characteristic equation. Finally, the validity and rationality of the theory are verified by numerical simulation.
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