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THE HOMOTOPY ANALYSIS METHOD IN BIFURCATION ANALYSIS OF DELAY DIFFERENTIAL EQUATIONS

ANDREA BEL

Departamento de Matemática, Universidad Nacional del Sur, CONICET, Av. Alem 1254, 8000 Bahía Blanca, Argentina

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and

WALTER REARTES

Departamento de Matemática, Universidad Nacional del Sur, Av. Alem 1254, 8000 Bahía Blanca, Argentina

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https://doi.org/10.1142/S0218127412300248Cited by:4 (Source: Crossref)

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, Neimark–Sacker, 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.

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