© 2017 World Scientific Publishing Company. We study the Hopf and the fold-Hopf bifurcations of the Rössler-type differential system [Equation presented here], with b≠0. We show that the classical Hopf bifurcation cannot be applied to this system for detecting the fold-Hopf bifurcation, which here is studied using the averaging theory. Our results show that a Hopf bifurcation takes place at the equilibrium (-ac/b,c/b,c/b) when c = a < 0. This Hopf bifurcation becomes a fold-Hopf bifurcation when c = a = 0.
|Journal||International Journal of Bifurcation and Chaos in Applied Sciences and Engineering|
|Publication status||Published - 1 May 2017|
- Rössler system
- averaging theory
- fold-Hopf bifurcation
- periodic orbits
- zero-Hopf bifurcation