Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method

Gen Ge and Wang Wei

Abstract and Applied Analysis, 2013, vol. 2013, 1-6

Abstract:

We investigate the Shilnikov sense homoclinicity in a 3D system and consider the dynamical behaviors in vicinity of the principal homoclinic orbit emerging from a third order simplified system. It depends on the application of the simplest normal form theory and further evolution of the Hopf-zero singularity unfolding. For the Shilnikov sense homoclinic orbit, the complex form analytic expression is accomplished by using the power series of the manifolds surrounding the saddle-focus equilibrium. Then, the second order Poincaré map in a generally analytical style helps to portrait the double pulse dynamics existing in the tubular neighborhood of the principal homoclinic orbit.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:294162

DOI: 10.1155/2013/294162

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