The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pad'e approximant

doi:10.1088/1674-1056/20/9/090202

Abstract In this paper, the extended Padé 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 ε 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.

Keywords: bifurcation Padé approximant strongly nonlinearity homoclinic and heteroclinic orbitals

Received: 05 January 2011
Revised: 16 May 2011
Accepted manuscript online:

PACS:	02.30.Hq	(Ordinary differential equations)
	47.20.Ky	(Nonlinearity, bifurcation, and symmetry breaking)
	82.40.Bj	(Oscillations, chaos, and bifurcations)

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Feng Jing-Jing(冯晶晶), Zhang Qi-Chang(张琪昌), and Wang Wei(王炜) The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pad'e approximant 2011 Chin. Phys. B 20 090202

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The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pad'e approximant

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