On the periodic orbit bifurcating from a zero Hopf bifurcation in systems with two slow and one fast variables

Isaac A. García, Jaume Llibre and Susanna Maza

Applied Mathematics and Computation, 2014, vol. 232, issue C, 84-90

Abstract: The Hopf bifurcation in slow-fast systems with two slow variables and one fast variable has been studied recently, mainly from a numerical point of view. Our goal is to provide an analytic proof of the existence of the zero Hopf bifurcation exhibited for such systems, and to characterize the stability or instability of the periodic orbit which borns in such zero Hopf bifurcation. Our proofs use the averaging theory.

Keywords: Zero Hopf bifurcation; Averaging theory; Singular perturbation (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:232:y:2014:i:c:p:84-90

DOI: 10.1016/j.amc.2013.12.184

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