CHAOS IN PERTURBED PLANAR NON-HAMILTONIAN INTEGRABLE SYSTEMS WITH SLOWLY-VARYINGANGLE PARAMETERS

Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (11): 1301-1305.

CHAOS IN PERTURBED PLANAR NON-HAMILTONIAN INTEGRABLE SYSTEMS WITH SLOWLY-VARYINGANGLE PARAMETERS

陈立群

Department of Mechanics, Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P.R.China

收稿日期:2000-07-19 修回日期:2001-04-08 出版日期:2001-11-18 发布日期:2001-11-18
通讯作者: LIU Zeng-rong
基金资助:
the National Natural Science Foundation of China (19782003);Shanghai Foundation of Science and Technology (98JC14032;98SHB1417)

CHAOS IN PERTURBED PLANAR NON-HAMILTONIAN INTEGRABLE SYSTEMS WITH SLOWLY-VARYINGANGLE PARAMETERS

CHEN Li-qun

Department of Mechanics, Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P.R.China

Received:2000-07-19 Revised:2001-04-08 Online:2001-11-18 Published:2001-11-18
Supported by:
the National Natural Science Foundation of China (19782003);Shanghai Foundation of Science and Technology (98JC14032;98SHB1417)

摘要/Abstract

摘要： The Melnikov method was extended to perturbed planar non-Hamiltonian integrable systems with slowly-varying angle parameters. Based on the analysis of the geometric structure of unperturbed systems, the condition of transversely homoclinic intersection was established. The generalized Melnikov function of the perturbed system was presented by applying the theorem on the differentiability of ordinary differential equation solutions with respect to parameters. Chaos may occur in the system if the generalized Melnikov function has simple zeros.

Abstract: The Melnikov method was extended to perturbed planar non-Hamiltonian integrable systems with slowly-varying angle parameters. Based on the analysis of the geometric structure of unperturbed systems, the condition of transversely homoclinic intersection was established. The generalized Melnikov function of the perturbed system was presented by applying the theorem on the differentiability of ordinary differential equation solutions with respect to parameters. Chaos may occur in the system if the generalized Melnikov function has simple zeros.

中图分类号:

O322

陈立群. CHAOS IN PERTURBED PLANAR NON-HAMILTONIAN INTEGRABLE SYSTEMS WITH SLOWLY-VARYINGANGLE PARAMETERS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(11): 1301-1305.

CHEN Li-qun . CHAOS IN PERTURBED PLANAR NON-HAMILTONIAN INTEGRABLE SYSTEMS WITH SLOWLY-VARYINGANGLE PARAMETERS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(11): 1301-1305.

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CHAOS IN PERTURBED PLANAR NON-HAMILTONIAN INTEGRABLE SYSTEMS WITH SLOWLY-VARYINGANGLE PARAMETERS

CHAOS IN PERTURBED PLANAR NON-HAMILTONIAN INTEGRABLE SYSTEMS WITH SLOWLY-VARYINGANGLE PARAMETERS

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