Existence, Number and Stability of Periodic Orbits Induced by Homoclinic Loops in Three-Dimensional Piecewise Linear Systems with an Admissible Saddle-Focus

被引：0

作者：

Wang, Lei ^{[1
]}

Yang, Xiao-Song ^{[2
]}

机构：

[1] Hefei Univ, Dept Math & Stat, Key Lab Appl Math & Artificial Intelligence Mech, Hefei 230601, Peoples R China

[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2023年 / 33卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Homoclinic loop; bifurcation; periodic orbit; stability; sink; saddle; piecewise linear system; GENERALIZED HOPF-BIFURCATION; LIMIT-CYCLE BIFURCATIONS; DIFFERENTIAL-SYSTEMS; HETEROCLINIC CYCLES; AVERAGING THEORY; SMOOTH SYSTEMS; LORENZ; FAMILY;

D O I：

10.1142/S0218127423500839

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a class of three-dimensional piecewise linear systems with an admissible saddle-focus, the existence of three kinds of homoclinic loops is shown. Moreover, the birth and number of the periodic orbits induced by homoclinic bifurcation are investigated, and various sufficient conditions are obtained to guarantee the appearance of only one periodic orbit, finitely many periodic orbits or countably infinitely many periodic orbits. Furthermore, the stability of these newborn periodic orbits is analyzed in detail and some conclusions are made about them to be periodic saddle orbits or periodic sinks. Finally, some examples are given.

引用

页数：24

共 18 条

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