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

作者：

Highlights：

• The norm forms of the double Hopf bifurcation for a general DDE is established.

• The van der Pol–Duffing oscillator with delayed position and velocity feedback is investigated.

• The dynamical classification near the double Hopf bifurcation point is studied.

• The stable periodic-doubling solutions and unstable three-dimensional torus are found.

摘要

•The norm forms of the double Hopf bifurcation for a general DDE is established.•The van der Pol–Duffing oscillator with delayed position and velocity feedback is investigated.•The dynamical classification near the double Hopf bifurcation point is studied.•The stable periodic-doubling solutions and unstable three-dimensional torus are found.

论文关键词：Double Hopf bifurcation,Normal forms,Center manifold reduction,van der Pol equation,Delayed position and velocity feedback

论文评审过程：Received 18 March 2015, Revised 26 May 2015, Accepted 6 June 2015, Available online 1 July 2015, Version of Record 1 July 2015.

论文官网地址：https://doi.org/10.1016/j.amc.2015.06.015