Approximations of the Heteroclinic Orbits Near a Double-Zero Bifurcation with Symmetry of Order Two. Application to a Liénard Equation

Author:

Rocşoreanu Carmen1ORCID,Sterpu Mihaela2

Affiliation:

1. Department of Statistics and Computer Science, University of Craiova, 13 A.I. Cuza, Craiova, Romania

2. Department of Mathematics, University of Craiova, 13 A.I. Cuza, Craiova, Romania

Abstract

A dynamical system possessing an equilibrium point with two zero eigenvalues is considered. We assume that a degenerate Bogdanov–Takens bifurcation with symmetry of order two is present and, in the parameter space, a curve of heteroclinic bifurcation values emerges from the codimension two bifurcation point. Using a blow-up transformation and a perturbation method, we obtain second order approximations both for the heteroclinic orbits and for the curve of heteroclinic bifurcation values. Applications of our results for the truncated normal form and for a Liénard equation are presented. Some numerical simulations illustrating the accuracy of our results are performed.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

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