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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/294162 |
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| author | Gen Ge Wang Wei |
| author_facet | Gen Ge Wang Wei |
| author_sort | Gen Ge |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-c81395b15c7442b39cea039de897e91c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c81395b15c7442b39cea039de897e91c2025-02-03T01:12:32ZengWileyAbstract 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 |
| spellingShingle | Gen Ge Wang Wei Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method Abstract and Applied Analysis |
| title | 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_short | Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method |
| title_sort | constructing the second order poincare map based on the hopf zero unfolding method |
| url | http://dx.doi.org/10.1155/2013/294162 |
| work_keys_str_mv | AT genge constructingthesecondorderpoincaremapbasedonthehopfzerounfoldingmethod AT wangwei constructingthesecondorderpoincaremapbasedonthehopfzerounfoldingmethod |