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Non-smooth bifurcation analysis of a piecewise linear chaotic circuit

Ji Ying Bi Qin-Sheng

Non-smooth bifurcation analysis of a piecewise linear chaotic circuit

Ji Ying, Bi Qin-Sheng
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Publishing process
  • Received Date:  22 February 2010
  • Accepted Date:  17 March 2010
  • Published Online:  15 November 2010

Non-smooth bifurcation analysis of a piecewise linear chaotic circuit

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

Abstract: The dynamics of a nonlinear capacitor circuit is investigated in this paper. The symmetric periodic solution and the chaotic attractor can be observed in numerical simulations. Furthermore, the generalized Jacobian matrix at the non-smooth boundaries is introduced to explore the non-smooth bifurcation mechanism for the periodic solutions. Discontinuous bifurcation in the combination of the Hopf bifurcation and the turning point bifurcation occurs at the non-smooth boundaries. Here, the Hopf bifurcation may result in a new frequency, which leads to periodic oscillation. With the variation of the parameter, the periodic symmetric solution oscillates more quickly, which can also be explained through non-smooth bifurcation, and the conclusion accord well with the numerical results.

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