The homotopy analysis method in bifurcation analysis of delay differential equations

Abstract

In this paper we apply the homotopy analysis method (HAM) to study the van der Pol equation with a linear delayed feedback. The paper focuses on the calculation of periodic solutions and associated bifurcations, Hopf, double Hopf, NeimarkSacker, etc. In particular, we discuss the behavior of the systems in the neighborhoods of double Hopf points. We demonstrate the applicability of HAM to the analysis of bifurcation and stability.