Existence and Number of Figure-Eight Loops in Planar Sector-Wise Linear Systems with Saddle–Saddle Dynamics

IF 1.9 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI:10.1142/s0218127423501985

Xiao-Juan Liu, Song-Mei Huan

引用次数: 0

Abstract

In this paper, we investigate the existence of one type of homoclinic double loops (i.e. figure-eight loops) in a family of planar sector-wise linear systems with saddle–saddle dynamics. We obtain necessary and sufficient conditions for the existence of a figure-eight loop. Moreover, we prove that such systems can have simultaneously three types of invariant sets: a figure-eight loop, a homoclinic loop and three different types of periodic orbits. We also provide an example to show that a crossing limit cycle can bifurcate from this figure-eight loop.

查看原文本刊更多论文

具有马鞍-马鞍动力学的平面扇形线性系统中图-八环路的存在与数量

本文研究了具有鞍鞍动力学的平面扇形线性系统族中一种同室双环（即八字环）的存在性。我们获得了图 8 循环存在的必要条件和充分条件。此外，我们还证明了这类系统可以同时具有三种类型的不变集：八字环、同轴环和三种不同类型的周期轨道。我们还提供了一个例子，说明从这个八字形环路可以分叉出一个交叉极限循环。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

International Journal of Bifurcation and Chaos 数学-数学跨学科应用

CiteScore

4.10

自引率

13.60%

发文量

237

审稿时长

2-4 weeks

期刊介绍： The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering. The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.