Normal forms of non-resonance and weak resonance double Hopf bifurcation in the retarded functional differential equations and applications

Heping Jiang and Yongli Song

Applied Mathematics and Computation, 2015, vol. 266, issue C, 1102-1126

Abstract: In this paper, we firstly present the general framework of calculation of normal forms of non-resonance and weak resonance double Hopf bifurcation for the general retarded functional differential equations by using the normal form theory of delay differential equations due to Faria and Magalha˜es. Then, the dynamical behavior of van der Pol–Duffing oscillator with delayed position and velocity feedback is considered. Specifically, the dynamical classification near the double Hopf bifurcation point is investigated by analyzing the obtained normal form. Finally, the numerical simulations support the theoretical results and present some interesting phenomena.

Keywords: Double Hopf bifurcation; Normal forms; Center manifold reduction; van der Pol equation; Delayed position and velocity feedback (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:266:y:2015:i:c:p:1102-1126

DOI: 10.1016/j.amc.2015.06.015

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