Abstract
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 language | English |
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Pages (from-to) | 779-790 |
Journal | Discrete and Continuous Dynamical Systems |
Volume | 30 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Jul 2011 |
Keywords
- Averaging theory
- Diffierential systems in dimension
- Hopf bifurcation