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Melnikov-Type Method for a Class of Discontinuous Planar Systems and Applications

Shuangbao Li

College of Science, Civil Aviation University of China, Tianjin 300300, P. R. China

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Wei Zhang

College of Mechanical Engineering, Beijing University of Technology, Beijing 100022, P. R. China

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, and

Yuxin Hao

College of Mechanical Engineering, Beijing Information Science and Technology University, Beijing 100192, P. R. China

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https://doi.org/10.1142/S0218127414500229Cited by:22 (Source: Crossref)

Abstract

In this paper, we extend the well-known Melnikov method for smooth systems to a class of periodic perturbed piecewise smooth planar system. We assume that the unperturbed system is a piecewise Hamiltonian system which possesses a piecewise smooth homoclinic solution transversally crossing the switching manifold. The Melnikov-type function is explicitly derived by using the Hamiltonian function to measure the distance of the perturbed stable and unstable manifolds. Finally, we apply the obtained results to study the chaotic dynamics of a concrete piecewise smooth system.

Keywords:

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