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

2016/09/29 by Huanhuan Tian, Tian, Huanhuan
Mathematics · Physics and Astronomy · #34C05 #34C07 #37G15 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #G.1.7 #Quantum chaos and dynamical systems #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.1609.09195

openalex publication_date 2016/09/29 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

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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