Classification of homoclinic tangencies for periodically perturbed systems

Yun Tang (), Fenghong Yang, Guanrong Chen and Tianshou Zhou

Chaos, Solitons & Fractals, 2006, vol. 28, issue 1, 76-89

Abstract: Classification of homoclinic tangencies for periodically perturbed systems is discussed. A relationship between the order of Melnikov function’s zeros and the harmonic components of a dynamical system is derived. By applying the singularity theory to the Melnikov function, possible types of homoclinic tangencies are studied for realization of the classification. In addition, certain multi-harmonically perturbed systems are investigated, showing the corresponding homoclinic bifurcation with their bifurcation diagrams.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:28:y:2006:i:1:p:76-89

DOI: 10.1016/j.chaos.2005.05.004

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