Existence and bifurcation of homoclinic orbits in planar piecewise linear systems

2009/07/01 by Xiao-Song Yang, Xiao‐Song Yang, Yang, Xiao-Song +3
Engineering · Mathematics · Physics and Astronomy · #34C23 #34C37(Primary) 37G99(Secondary) #Advanced Differential Equations and Dynamical Systems #Control and Dynamics of Mobile Robots #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #math.DS #msc:34C23

paper · pdf · doi:10.48550/arxiv.0907.0055

17pages,20figures

arxiv created 2009/07/01 · openalex publication_date 2009/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The existence and bifurcation of homoclinic orbits in planar piecewise linear homogeneous systems with two regions separated by a discontinuity boundary are investigated in this paper. In addition, existence of periodic orbits and stability of the origin are also discussed without the assumption of continuity for the planar piecewise linear homogeneous systems.

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