Dynamics due to non-resonant double Hopf bifurcationin in van del Pol-Duffing system with delayed position feedback

Abstract

In this paper, the van der Pol-Duffing system with delayed position feedback is investigated A critical point with 1: √2 frequency ratio is obtained. The center manifold reduction (CMR) is employed to classify various solutions bifurcating from the point. The approximate expressions provided by the CMR are valid for values of the time delay and feedback gain close to the double Hopf point but invalid for those of the bifurcation parameters far from the bifurcation point. A called perturbation-incremental scheme (PIS) is proposed to overcome such disadvantage. The consistency between numerical and PIS solutions shows the PIS is efficient. The analytical approximation derived from the PIS can reach any required accuracy. © 2007 Springer.