Multi-pulse Orbits and Homoclinic Trees in a Non-autonomous Resonant Hamiltonian System
In this study, we develop the energy-phase method to deal with the high-dimensional non-autonomous nonlinear dynamical systems. Our generalized energy-phase method applies to integrable, two-degree-of freedom non-autonomous resonant Hamiltonian systems. As an example, we investigate the multi-pulse...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2016-01-01
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| Series: | MATEC Web of Conferences |
| Online Access: | http://dx.doi.org/10.1051/matecconf/20164503004 |
| _version_ | 1818725575307558912 |
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| author | Zhou Sha Zhang Wei Yu Tian-jun |
| author_facet | Zhou Sha Zhang Wei Yu Tian-jun |
| author_sort | Zhou Sha |
| collection | DOAJ |
| description | In this study, we develop the energy-phase method to deal with the high-dimensional non-autonomous nonlinear dynamical systems. Our generalized energy-phase method applies to integrable, two-degree-of freedom non-autonomous resonant Hamiltonian systems. As an example, we investigate the multi-pulse orbits and homoclinic trees for a parametrically excited, simply supported rectangular thin plate of two-mode approximation. In both the Hamiltonian and dissipative case we find homoclinic trees, which describe the repeated bifurcations of multi-pulse solutions, and we present visualizations of these complicated structures. |
| first_indexed | 2024-12-17T21:44:29Z |
| format | Article |
| id | doaj.art-f0cf95cd8a844ccc95b31256b1e93362 |
| institution | Directory Open Access Journal |
| issn | 2261-236X |
| language | English |
| last_indexed | 2024-12-17T21:44:29Z |
| publishDate | 2016-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | MATEC Web of Conferences |
| spelling | doaj.art-f0cf95cd8a844ccc95b31256b1e933622022-12-21T21:31:31ZengEDP SciencesMATEC Web of Conferences2261-236X2016-01-01450300410.1051/matecconf/20164503004matecconf_icmm2016_03004Multi-pulse Orbits and Homoclinic Trees in a Non-autonomous Resonant Hamiltonian SystemZhou ShaZhang WeiYu Tian-junIn this study, we develop the energy-phase method to deal with the high-dimensional non-autonomous nonlinear dynamical systems. Our generalized energy-phase method applies to integrable, two-degree-of freedom non-autonomous resonant Hamiltonian systems. As an example, we investigate the multi-pulse orbits and homoclinic trees for a parametrically excited, simply supported rectangular thin plate of two-mode approximation. In both the Hamiltonian and dissipative case we find homoclinic trees, which describe the repeated bifurcations of multi-pulse solutions, and we present visualizations of these complicated structures.http://dx.doi.org/10.1051/matecconf/20164503004 |
| spellingShingle | Zhou Sha Zhang Wei Yu Tian-jun Multi-pulse Orbits and Homoclinic Trees in a Non-autonomous Resonant Hamiltonian System MATEC Web of Conferences |
| title | Multi-pulse Orbits and Homoclinic Trees in a Non-autonomous Resonant Hamiltonian System |
| title_full | Multi-pulse Orbits and Homoclinic Trees in a Non-autonomous Resonant Hamiltonian System |
| title_fullStr | Multi-pulse Orbits and Homoclinic Trees in a Non-autonomous Resonant Hamiltonian System |
| title_full_unstemmed | Multi-pulse Orbits and Homoclinic Trees in a Non-autonomous Resonant Hamiltonian System |
| title_short | Multi-pulse Orbits and Homoclinic Trees in a Non-autonomous Resonant Hamiltonian System |
| title_sort | multi pulse orbits and homoclinic trees in a non autonomous resonant hamiltonian system |
| url | http://dx.doi.org/10.1051/matecconf/20164503004 |
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