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2010 | OriginalPaper | Chapter

9. Perturbations and Hopf Bifurcation of a Discontinuous Limit Cycle

Author : Marat Akhmet

Published in: Principles of Discontinuous Dynamical Systems

Publisher: Springer New York

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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.

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Metadata
Title
Perturbations and Hopf Bifurcation of a Discontinuous Limit Cycle
Author
Marat Akhmet
Copyright Year
2010
Publisher
Springer New York
Book
Principles of Discontinuous Dynamical Systems

Print ISBN: 978-1-4419-6580-6

Electronic ISBN: 978-1-4419-6581-3

Copyright Year: 2010

DOI
https://doi.org/10.1007/978-1-4419-6581-3_9

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