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Perturbations and Hopf Bifurcation of a Discontinuous Limit Cycle

In: Principles of Discontinuous Dynamical Systems

Author

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  • Marat Akhmet

    (Middle East Technical University, Department of Mathematics)

Abstract

This chapter is organized in the following manner. In the first section, we give the description of the systems under consideration and prove the theorem of existence of foci and centers of the nonperturbed system. The main subject of Sect. 9.2 is foci of the perturbed equation. The noncritical case is considered. In Sect. 9.3, the problem of distinguishing between the center and the focus is solved. Bifurcation of a periodic solution is investigated in Sect. 9.4. The last section consists of examples illustrating the bifurcation theorem.

Suggested Citation

  • Marat Akhmet, 2010. "Perturbations and Hopf Bifurcation of a Discontinuous Limit Cycle," Springer Books, in: Principles of Discontinuous Dynamical Systems, chapter 0, pages 139-154, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-6581-3_9
    DOI: 10.1007/978-1-4419-6581-3_9
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