Existence and bifurcation of homoclinic orbits in planar piecewise linear systems
Xiao-Song Yang, Songmei Huan
TL;DR
This paper investigates the existence, bifurcation, and stability of homoclinic and periodic orbits in planar piecewise linear systems with discontinuities, expanding understanding without assuming system continuity.
Contribution
It provides new conditions for homoclinic orbit existence and bifurcation in discontinuous planar linear systems, and analyzes stability and periodic orbits.
Findings
Homoclinic orbits exist under specific parameter conditions.
Bifurcation phenomena are characterized in the discontinuous setting.
Stability of the system's origin is determined without continuity assumptions.
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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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Quantum chaos and dynamical systems · Control and Dynamics of Mobile Robots