2Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 83, pp. 1-57.

Title: Global analysis on a continuous planar piecewise linear differential system with three zones
       
Authors: Man Jia (Central South Univ., Changsha, Hunan, China)
         Youfeng Su (Fuzhou Univ., Fujian, China)
         Hebai Chen (Central South Univ., Changsha, Hunan, China)

Abstract:
This article concerns the global dynamics of a continuous planar piecewise
linear differential system with three zones.
We give global phase portraits in the Poincare disc and
classify bifurcation diagrams under certain parametric conditions,
when the dynamics of central linear zone is anti-saddle.
Rich dynamical behaviors are demonstrated, from which we observe homoclinic loops 
appearing in three linear zones and limit cycles occurring in three linear zones 
which surround a node or node-focus.

Submitted June 6, 2023. Published December 10, 2023.
Math Subject Classifications: 34C05, 34C23, 37G15, 37G20.
Key Words: Piecewise linear system; global phase portrait; bifurcation; invariant manifold; limit cycle; homoclinic loop.