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.
|Journal||Discrete and Continuous Dynamical Systems|
|Publication status||Published - 1 Jul 2011|
- Averaging theory
- Diffierential systems in dimension
- Hopf bifurcation
Llibre, J., & Valls, C. (2011). Hopf bifurcation for some analytic differential systems in ℝ3 via averaging theory. Discrete and Continuous Dynamical Systems, 30(3), 779-790. https://doi.org/10.3934/dcds.2011.30.779