Sliding Hopf bifurcation in interval systems

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2017Embargo end date: 01 Jul 2015Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Discrete and Continuous Dynamical Systems, volume 37, pages 3,545-3,566 (issn: 1078-0947, eissn: 1553-5231,

Copyright policy )Funded by:NSF | Stabilization of Periodic...

Authors: Hooton, Edward; Balanov, Zalman; Krawcewicz, Wieslaw; Rachinskii, Dmitrii;

doi: 10.3934/dcds.2017152 , 10.48550/arxiv.1507.08596

arXiv: 1507.08596

Sliding Hopf bifurcation in interval systems

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Abstract

In this paper, the equivariant degree theory is used to analyze the occurrence of the Hopf bifurcation under effectively verifiable mild conditions. We combine the abstract result with standard interval polynomial techniques based on Kharitonov's theorem to show the existence of a branch of periodic solutions emanating from the equilibrium in the settings relevant to robust control. The results are illustrated with a number of examples.

22 pages

Related Organizations

The University of Texas at Dallas
United States

Keywords

non-local branch, Kharitonov's theorem, 37G15, Dynamical Systems (math.DS), interval polynomial, Dynamical aspects of symmetries, equivariant bifurcation theory, Optimization and Control (math.OC), Bifurcations of limit cycles and periodic orbits in dynamical systems, FOS: Mathematics, zero exclusion principle, Hopf bifurcation, Mathematics - Dynamical Systems, Mathematics - Optimization and Control, \(S^1\)-degree

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