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...

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Bibliographic Details
Published inMATEC Web of Conferences Vol. 45; p. 3004
Main Authors Zhou, Sha, Zhang, Wei, Yu, Tian-jun
Format Journal Article Conference Proceeding
LanguageEnglish
Published Les Ulis EDP Sciences 01.01.2016
Subjects
Bifurcations
Chaos theory
Hamiltonian functions
Nonlinear systems
Thin plates
Trees
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Summary: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.
ISSN:2261-236X
2274-7214
2261-236X
DOI:10.1051/matecconf/20164503004