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, issue 1

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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https://doi.org/10.1155/2013/294162

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:294162

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