Applied Mathematics and Mechanics

, Volume 22, Issue 11, pp 1301–1305 | Cite as

Chaos in perturbed planar non-Hamiltonian integrable systems with slowly-varying angle parameters

  • Chen Li-qun


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.

Key words

Melnikov method perturbed integrable system transversely homoclinic chaos 

CLC number



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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Chen Li-qun
    • 1
    • 2
  1. 1.Department of MechanicsShanghai UniversityShanghaiP R China
  2. 2.Shanghai Institute of Applied Mathematics and MechanicsShanghaiP R China

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