Hopf Bifurcation of Duffing-Van der pol System

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Journal of Vibration and Shock ›› 2010, Vol. 29 ›› Issue (7) : 204-209.

论文

Hopf Bifurcation of Duffing-Van der pol System

FU Wu-jiu

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Abstract

Take Duffing equation as a non-perturbed Hamiltonian system in Duffing-van der pol equation ,its four conditions is solved rigorously.Subharmonic bifurcation of the Duffing-van der pol system is studied by sub-Melnikov method,Hopf bifurcation conditions are obtained for the Duffing-van der pol system. Hopf bifurcation curves are geted to base of the bifurcation conditions in the parameter space. on the bifurcation curve we take the parameters that do numerical simulate, to obtain odd number order and even number order Hopf bifurcations in correspondence with our theoretical analysis.