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Non-smooth bifurcation in nonlinear electrical circuits with multiple switching boundaries

Zhang Yin Bi Qin-Sheng

Non-smooth bifurcation in nonlinear electrical circuits with multiple switching boundaries

Zhang Yin, Bi Qin-Sheng
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  • Received Date:  29 September 2010
  • Accepted Date:  18 October 2010
  • Published Online:  15 July 2011

Non-smooth bifurcation in nonlinear electrical circuits with multiple switching boundaries

  • 1. Faculty of Science, Jiangsu University, Zhenjiang 212013, China

Abstract: The fast-slow dynamics of a nonlinear electrical circuit with multiple switching boundaries is investigated in this paper. For suitable parameters, periodic bursting phenomenon can be observed. The full system can be divided into slow and fast subsystems because of the difference between variational speeds of state variables. According to the slow-fast analysis, the slow variable, which modulates the behavior of the system, can be treated as a quasi-static bifurcation parameter for the fast subsystem to analyze the stabilities of equilibrium points in different areas of vector field. The bifurcation is dependent on the switching boundary in the vector field. In particular, for the two-time scale non-smooth system with fast-slow effect, the bifurcation of fast subsystem is determined by the characteristics of equilibrium points on both sides of the switching boundary. Furthermore, the generalized Jacobian matrix at the non-smooth boundary is introduced to explore the type of non-smooth bifurcation (i.e., multiple crossing bifurcation) in the fast subsystem, which can also be used to explain the mechanism for symmetric bursting phenomenon of the full system.

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