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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.

Keywords

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