Hopf bifurcation for some analytic differential systems in ℝ3 via averaging theory

Jaume Llibre, Clàudia Valls

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11 Citations (Scopus)


We study the Hopf bifurcation from the singular point with eigen-values a ε ± b i and c ε located at the origen of an analytic diffierential system of the form ẋ = f(x), where x ∈ ℝ3. Under convenient assumptions we prove that the Hopf bifurcation can produce 1, 2 or 3 limit cycles. We also characterize the stability of these limit cycles. The main tool for proving these results is the averaging theory of first and second order.
Original languageEnglish
Pages (from-to)779-790
JournalDiscrete and Continuous Dynamical Systems
Issue number3
Publication statusPublished - 1 Jul 2011


  • Averaging theory
  • Diffierential systems in dimension
  • Hopf bifurcation


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