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Periodic Orbits of Linear Filippov Systems with a Line of Discontinuity

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Abstract

In this paper we consider periodic orbits of planar linear Filippov systems with a line of discontinuity. Unlike many publications researching only the maximum number of crossing periodic orbits, we investigate not only the number and configuration of sliding periodic orbits, but also the coexistence of sliding periodic orbits and crossing ones. Firstly, we prove that the number of sliding periodic orbits is at most 2, and give all possible configurations of one or two sliding periodic orbits. Secondly, we prove that two sliding periodic orbits coexist with at most one crossing periodic orbit, and one sliding periodic orbit can coexist with two crossing ones.

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  1. School of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Tao Li & Xingwu Chen

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  1. Tao Li
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  2. Xingwu Chen
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Correspondence to Xingwu Chen.

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Li, T., Chen, X. Periodic Orbits of Linear Filippov Systems with a Line of Discontinuity. Qual. Theory Dyn. Syst. 19, 47 (2020). https://doi.org/10.1007/s12346-020-00384-3

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