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

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

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 si...

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Main Authors: Gen Ge, Wang Wei
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/294162
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spelling doaj-c81395b15c7442b39cea039de897e91c2020-11-24T21:13:47ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/294162294162Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding MethodGen Ge0Wang Wei1School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin 300072, ChinaDepartment of Mechanics, Tianjin University, Tianjin 300072, ChinaWe 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.http://dx.doi.org/10.1155/2013/294162
collection DOAJ
language English
format Article
sources DOAJ
author Gen Ge
Wang Wei
spellingShingle Gen Ge
Wang Wei
Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method
Abstract and Applied Analysis
author_facet Gen Ge
Wang Wei
author_sort Gen Ge
title Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method
title_short Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method
title_full Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method
title_fullStr Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method
title_full_unstemmed Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method
title_sort constructing the second order poincaré map based on the hopf-zero unfolding method
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description 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.
url http://dx.doi.org/10.1155/2013/294162
work_keys_str_mv AT genge constructingthesecondorderpoincaremapbasedonthehopfzerounfoldingmethod
AT wangwei constructingthesecondorderpoincaremapbasedonthehopfzerounfoldingmethod
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