The discontinuous planar piecewise linear system with two nodes has at most two limit cycles
Dynamical Systems
2025-06-10 v1 Classical Analysis and ODEs
Abstract
This paper investigates the multiplicity and the number of limit cycles for planar piecewise linear system divided into two regions by a straight line and each linear subsystem has a node. Through constructing Poincare half maps and a successor function, and analyzing the properties of the successor function, we can derive that this system has at most two limit cycles, counting the multiplicities of limit cycles.
Cite
@article{arxiv.2506.07716,
title = {The discontinuous planar piecewise linear system with two nodes has at most two limit cycles},
author = {Lu Chen and Changjian Liu},
journal= {arXiv preprint arXiv:2506.07716},
year = {2025}
}
Comments
29 pages,6 figures