On the Number of Limit Cycles Bifurcated from a Near-Hamiltonian System with a Double Homoclinic Loop of Cuspidal Type Surrounded by a Heteroclinic Loop

被引：3

作者：

Moghimi, Pegah ^{[1
]}

Asheghi, Rasoul ^{[1
]}

Kazemi, Rasool ^{[2
]}

机构：

[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran

[2] Univ Kashan, Dept Math Sci, Kashan 8731753153, Iran

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2018年 / 28卷 / 01期

关键词：

Limit cycle; bifurcation; Hamiltonian system; Melnikov function; asymptotic expansion; SMALL PERTURBATIONS; FINITE CYCLICITY; GRAPHICS; SADDLE;

D O I：

10.1142/S0218127418500049

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the number of bifurcated limit cycles from some polynomial systems with a double homoclinic loop passing through a nilpotent saddle surrounded by a heteroclinic loop, and obtain some new results on the lower bound of the maximal number of limit cycles for these systems. In particular, we study the bifurcation of limit cycles in the following system: <(x) over dot> = y, <(y) over dot> = x(3) (x(2) - 1) (x(2) - 4) + epsilon f(x)y, where f(x) is a polynomial of degree 8 <= n <= 10.

引用

页数：21

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