Abstract
© 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.
Original language | English |
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Article number | 1750068 |
Journal | International Journal of Bifurcation and Chaos in Applied Sciences and Engineering |
Volume | 27 |
Issue number | 5 |
DOIs | |
Publication status | Published - 1 May 2017 |
Keywords
- Rössler system
- averaging theory
- fold-Hopf bifurcation
- periodic orbits
- zero-Hopf bifurcation