Non-smooth bifurcations in a double-scroll circuit with periodic excitation

doi:10.1088/1674-1056/20/1/010504

Abstract The fast-slow effect can be observed in a typical non-smooth electric circuit with order gap between the natural frequency and the excitation frequency. Numerical simulations are employed to show complicated behaviours, especially different types of busting phenomena. The bifurcation mechanism for the bursting solutions is analysed by assuming the forms of the solutions and introducing the generalized Jacobian matrix at the non-smooth boundaries, which can also be used to account for the evolution of the complicated structures of the phase portraits with the variation of the parameter. Period-adding bifurcation has been explored through the computation of the eigenvalues related to the solutions. At the non-smooth boundaries the so-called 'single crossing bifurcation' can occur, corresponding to the case where the eigenvalues jump only once across the imaginary axis, which leads the periodic burster to have a quasi-periodic oscillation.

Keywords: Matsumoto's circuit non-smooth bifurcation fast-slow effect bursting

Received: 07 May 2010
Revised: 10 June 2010
Accepted manuscript online:

PACS:	05.45.Ac	(Low-dimensional chaos)
	05.45.Pq	(Numerical simulations of chaotic systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10972091 and 10872080).

Cite this article:

Zhang Yin(张银)and Bi Qin-Sheng(毕勤胜) Non-smooth bifurcations in a double-scroll circuit with periodic excitation 2011 Chin. Phys. B 20 010504

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Non-smooth bifurcations in a double-scroll circuit with periodic excitation

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