Perturbations and Hopf Bifurcation of a Discontinuous Limit Cycle

Marat Akhmet ()
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Marat Akhmet: Middle East Technical University, Department of Mathematics

Chapter Chapter 9 in Principles of Discontinuous Dynamical Systems, 2010, pp 139-154 from Springer

Abstract: 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.

Date: 2010
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DOI: 10.1007/978-1-4419-6581-3_9

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