Multi-pulse Orbits and Homoclinic Trees in a Non-autonomous Resonant Hamiltonian System
1 Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, 100124, China
2 Beijing University of Technology, College of Mechanical Engineering, 100124, China
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.
© Owned by the authors, published by EDP Sciences, 2016
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