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arXiv · 1609.09195

Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order 2

Huanhuan Tian
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Abstract

In this paper, we deal with limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order 2 by studying expansions of the first order Melnikov functions near the loop and coefficients in these expansions. More precisely, we prove that the perturbed system can have 11, 13, 14 or 16 limit cycles in a neighborhood of the loop under certain conditions. Finally, we give an example to illustrate the effectiveness of our main results.

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BibTeXRIS

Huanhuan Tian. 2016-09-29. Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order 2. https://arxiv.org/abs/1609.09195

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