Title: ON THE HOPF–PITCHFORK BIFURCATION IN THE CHUA'S EQUATION
Abstract: We study some periodic and quasiperiodic behaviors exhibited by the Chua's equation with a cubic nonlinearity, near a Hopf–pitchfork bifurcation. We classify the types of this bifurcation in the nondegenerate cases, and point out the presence of a degenerate Hopf–pitchfork bifurcation. In this degenerate situation, analytical and numerical study shows a diversity of bifurcations of periodic orbits. We find a secondary Hopf bifurcation of periodic orbits, where invariant torus appears. This secondary Hopf bifurcation is bounded by a Takens–Bogdanov bifurcation of periodic orbits. Here, a sequence of period-doubling bifurcations of invariant tori is detected. Resonance phenomena are also analyzed. In the case of strong resonance 1:4, we show a new sequence of period-doubling bifurcations of 4T invariant tori.
Publication Year: 2000
Publication Date: 2000-02-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 30
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot