Zero-Hopf bifurcation in a Chua system

Rodrigo D. Euzébio, Jaume Llibre

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13 Citations (Scopus)

Abstract

© 2017 Elsevier Ltd A zero-Hopf equilibrium is an isolated equilibrium point whose eigenvalues are ±ωi≠0 and 0. In general for a such equilibrium there is no theory for knowing when it bifurcates some small-amplitude limit cycles moving the parameters of the system. Here we study the zero-Hopf bifurcation using the averaging theory. We apply this theory to a Chua system depending on 6 parameters, but the way followed for studying the zero-Hopf bifurcation can be applied to any other differential system in dimension 3 or higher. In this paper first we show that there are three 4-parameter families of Chua systems exhibiting a zero-Hopf equilibrium. After, by using the averaging theory, we provide sufficient conditions for the bifurcation of limit cycles from these families of zero-Hopf equilibria. From one family we can prove that 1 limit cycle bifurcates, and from the other two families we can prove that 1, 2 or 3 limit cycles bifurcate simultaneously.
Original languageEnglish
Pages (from-to)31-40
JournalNonlinear Analysis: Real World Applications
Volume37
DOIs
Publication statusPublished - 1 Oct 2017

Keywords

  • Averaging theory
  • Chua system
  • Periodic orbit
  • Zero Hopf bifurcation

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