The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pade approximant
In this paper, the extended Pade 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...
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Published in | Chinese physics B Vol. 20; no. 9; pp. 19 - 29 |
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Format | Journal Article |
Language | English |
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IOP Publishing
01.09.2011
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ISSN | 1674-1056 2058-3834 |
DOI | 10.1088/1674-1056/20/9/090202 |
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Abstract | In this paper, the extended Pade 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 ~ 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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AbstractList | In this paper, the extended Pade 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 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. |
Author | 冯晶晶 张琪昌 王炜 |
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Cites_doi | 10.1006/jsvi.1995.0218 10.7498/aps.58.7525 10.1007/s10409-009-0276-0 10.1088/1674-1056/18/5/009 10.1088/1009-1963/15/3/012 10.1016/j.jappmathmech.2005.01.004 10.1006/jsvi.1999.2669 10.1023/A:1008269608568 10.1016/j.jsv.2008.11.015 10.1007/978-1-4757-4067-7 10.1088/0256-307X/25/5/105 10.1088/1009-1963/11/5/306 |
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Notes | In this paper, the extended Pade 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 ~ 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. Feng Jing-Jing Zhang Qi-Chang and Wang Wei a) Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300072, China b) Tianjin Key Labortory of Nonlinear Dynamics and Chaos Control, Tianjin University, Tianjin 300072, China c) State Key Laboratory of Engines, Tianjin University, Tianfin 300072, China 11-5639/O4 bifurcation, Pade approximant, strongly nonlinearity, homoclinic and heteroclinic orbitals ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 ObjectType-Article-1 ObjectType-Feature-2 |
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References | 11 12 Zhang Q C (14) 2008; 57 15 Wiggins S (2) 1990 16 Baker Jr G A (18) 1981 Guckenheimer J (1) 1993 Jiang B (8) 2010; 59 19 Zhang Q C (13) 2008; 25 Baker Jr G A (17) 1970 Chen J J (6) 2009; 58 Wang Z (7) 2011; 60 Yang Z Q (4) 2006; 15 Liu N (3) 2009; 18 Melnikov V K (9) 1963; 12 Chen X W (5) 2002; 11 Emaci E (10) 1997; 13 |
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SubjectTerms | Approximants Asymmetry Boundary value problems Construction Dynamical systems Mathematical analysis Nonlinear dynamics Nonlinearity Padé逼近 不对称 异宿轨道 强非线性系统 边界值问题 非线性动力系统 非线性方程 非自治系统 |
Title | The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pade approximant |
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