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Phase Portraits of the Discontinuous Planar Piecewise Linear Differential Systems of Focus-Center Type

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Abstract

In this paper, we study the global phase portraits of the discontinuous planar piecewise linear differential system of the focus-center type and the center-center type with a straight line of separation. We obtain sufficient conditions for the existence and number of the crossing limit cycles and sliding limit cycles of the system. We prove the system of focus-center type and center-center type have 45 and 15 topologically different global phase portraits, respectively.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guizhou University, Guiyang, 550025, China

    Li Xiong & Kuilin Wu

  2. School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou, 510320, China

    Shimin Li

Authors
  1. Li Xiong
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  2. Kuilin Wu
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  3. Shimin Li
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Correspondence to Kuilin Wu.

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Supported by NSFC (11661017) and Science and Technology Plan Project of Guizhou Province(ZK[2022]G118)

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Xiong, L., Wu, K. & Li, S. Phase Portraits of the Discontinuous Planar Piecewise Linear Differential Systems of Focus-Center Type. Qual. Theory Dyn. Syst. 21, 78 (2022). https://doi.org/10.1007/s12346-022-00612-y

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  • DOI: https://doi.org/10.1007/s12346-022-00612-y

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