We study the Hopf bifurcation occurring in polynomial quadratic vector fields in ℝ3. By applying the averaging theory of second order to these systems we show that at most 3 limit cycles can bifurcate from a singular point having eigenvalues of the form ± bi and 0. We provide an example of a quadratic polynomial differential system for which exactly 3 limit cycles bifurcate from a such singular point.
|Journal||Discrete and Continuous Dynamical Systems|
|Publication status||Published - 1 Dec 2009|
- Averaging theory
- Hopf bifurcation
- Limit cycle