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arXiv · 2506.07716

The discontinuous planar piecewise linear system with two nodes has at most two limit cycles

Lu Chen·Changjian Liu
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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.

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Lu Chen, Changjian Liu. 2025-06-09. The discontinuous planar piecewise linear system with two nodes has at most two limit cycles. https://arxiv.org/abs/2506.07716

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