Existence of periodic orbits in three-dimensional piecewise linear systems

TL;DR

This paper investigates the conditions under which periodic orbits exist in three-dimensional continuous piecewise linear homogeneous systems with two zones, providing a complete characterization of their existence.

Contribution

It offers a necessary and sufficient condition for the existence of periodic orbits in such systems, expanding the understanding of their dynamical behavior.

Findings

Derived a necessary and sufficient condition for periodic orbits

Connected invariant cone results to periodic orbit existence

Enhanced understanding of three-dimensional piecewise linear systems

Abstract

Based on the results about the invariant cones appeared in the literature this paper analyses the existence of periodic orbits in three-dimensional continuous piecewise linear homogeneous systems with two zones, and a necessary and sufficient condition for the existence of periodic orbits of such systems is given.