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2013 Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method
Gen Ge, Wang Wei
Abstr. Appl. Anal. 2013(SI41): 1-6 (2013). DOI: 10.1155/2013/294162


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.


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Gen Ge. Wang Wei. "Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method." Abstr. Appl. Anal. 2013 (SI41) 1 - 6, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1296.34119
MathSciNet: MR3116361
Digital Object Identifier: 10.1155/2013/294162

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI41 • 2013
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