Qian-Qian Han, Song-Mei Huan
Abstract:
In this article, we study the global dynamics of a special class of
planar sector-wise linear differential systems with two subsystems being
the same except for their equilibriums.
Taking the position of one equilibrium as the bifurcation parameter, we
provide a complete analysis about sliding cycle bifurcation and sliding
homoclinic bifurcation. Moreover, we obtain the existence of all important
separatrix orbits and their dependence on the bifurcation parameter,
including sliding heteroclinic orbit, heteroclinic cycle, limit cycle,
sliding homoclinic cycle and sliding cycle.
Submitted April 2, 2024. Published September 30, 2024.
Math Subject Classifications: 34C23, 34C60, 34C37.
Key Words: Sector-wise linear systems; sliding cycle bifurcation;
sliding homoclinic bifurcation; heteroclinic cycle; non-regular point.
DOI: 10.58997/ejde.2024.57
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Qian-Qian Han School of Mathematics and Statistics North China University of Water Resources and Electric Power Zhengzhou, Henan 450046, China email: hanqianqian@ncwu.edu.cn |
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| Song-Mei Huan School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Key Laboratory of Engineering Modeling and Scientific Computing Wuhan, Hubei 430074, China email: smhuan@hust.edu.cn |
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