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The oscillations of a switching electrical circuit and the mechanism of non-smooth bifurcations

Wu Tian-Yi Zhang Zheng-Di Bi Qin-Sheng

The oscillations of a switching electrical circuit and the mechanism of non-smooth bifurcations

Wu Tian-Yi, Zhang Zheng-Di, Bi Qin-Sheng
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Publishing process
  • Received Date:  13 July 2011
  • Accepted Date:  05 April 2012
  • Published Online:  05 April 2012

The oscillations of a switching electrical circuit and the mechanism of non-smooth bifurcations

  • 1. Facuity of Science, Jiangsu University, Zhenjiang 212013, China;
  • 2. Zhenjiang Watercraft College, Zhenjiang 212003, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 20976075,10972091).

Abstract: The complicated dynamical evolution of a circuit system composed of two Rayleigh-types subsystems, which are switched by a periodic switch and a threshold controller, is investigated. Through the analysis of the subsystem equilibrium points, the conditions for Fold bifurcation and Hopf bifurcation in the parameter space are given respectively. The distribution of the generalized Jacobian eigenvalues varying with auxiliary parameter at the switching boundary is presented. Then the possible bifurcation behaviors of the system at the switching boundary are obtained. The mechanisms of the different behaviors of the system are discussed. It is pointed that the trajectories of the system have two kinds of turning points, which are determined by the periodic switch and the threshold controller respectively. Meanwhile, the multiple collisions between the trajectories and the non-smooth boundary may lead the system to change from chaos to period-adding bifurcation.

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