The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pad'e approximant |
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| Authors: | Feng Jing-Jing Zhang Qi-Chang Wang Wei |
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| Affiliation: | Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300072, China;Tianjin Key Labortory of Nonlinear Dynamics and Chaos Control, Tianjin University, Tianjin 300072, China; State Key Laboratory of Engines, Tianjin University, Tianjin 300072, China |
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| Abstract: | In this paper, the extended Pad'e approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the autonomous system, and the nonautonomous system equations with quadratic and cubic nonlinearities are considered. The disturbance parameter varepsilon is not limited to being small. The ranges of the values of the linear and the nonlinear term parameters, which are variables, can be determined when the boundary values are satisfied. New conditions for the potentiality and the convergence are posed to make it possible to solve the boundary-value problems formulated for the orbitals and to evaluate the initial amplitude values. |
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| Keywords: | bifurcation Pad'e approximant strongly nonlinearity homoclinic and heteroclinic orbitals |
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