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

García, I. A. (Isaac A.); Llibre, Jaume; Maza Sabido, Susanna

doi:https://doi.org/10.1016/j.amc.2013.12.184

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Issue date

2014

Author

García, I. A. (Isaac A.)

Llibre, Jaume

Maza Sabido, Susanna

Suggested citation

García, I. A. (Isaac A.); Llibre, Jaume; Maza Sabido, Susanna; . (2014) . On the periodic orbit bifurcating from a Hopf bifurcation in systems with two slow and one fast variables. Applied Mathematics and Computation, 2014, vol. 232, p. 84-90. https://doi.org/10.1016/j.amc.2013.12.184.

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.

URI

http://hdl.handle.net/10459.1/60380

DOI

https://doi.org/10.1016/j.amc.2013.12.184

Is part of

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