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Relaxation bursting and the mechanism of four-dimensional Chua's circuit with multiple interfaces

Zhang Xiao-Fang Chen Xiao-Ke Bi Qin-Sheng

Relaxation bursting and the mechanism of four-dimensional Chua's circuit with multiple interfaces

Zhang Xiao-Fang, Chen Xiao-Ke, Bi Qin-Sheng
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Publishing process
  • Received Date:  31 May 2012
  • Accepted Date:  26 July 2012
  • Published Online:  05 January 2013

Relaxation bursting and the mechanism of four-dimensional Chua's circuit with multiple interfaces

  • 1. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 10972091, 20976075) and the Senior Qualified Personal Foundation of Jiangsu University, China (Grant No. 10JDG144).

Abstract: Based on the classical Chua's circuit, a four-dimensional Generalized Chua's circuit with multiple interfaces is established by introducing feedback elements. For the appropriate condition, there exists a difference in order of magnitude between the variables of state and a fast-slow coupled system, thereby forming a fast- and slow-coupled system at time scale. Analyzing the equilibrium points and the characteristics of the fast subsystems, and combining the theory of Clarke differential inclusions, the singularities on the non-smooth boundaries are explored. Two types of periodic bursting phenomena for different conditions are presented. Fast-slow analysis is employed to explore the special cluster phenomenon while the system trajectory passes across multiple interfaces. The coexisting different bursting mechanisms for the case with multiple attractors are explored in detail, while the influence of non-smooth bifurcations on bursting behavior is revealed.

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