JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (12): 114-121.doi: 10.6040/j.issn.1671-9352.0.2023.202

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Periodic solutions of a non-autonomous piecewise bilinear system

FAN Jianhang, WU Kuilin*   

  1. School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China
  • Published:2024-12-12

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Abstract: The existence of periodic solutions of a non-autonomous piecewise bilinear system is concerned. First, a bounded closed domain is constructed such that any orbit of the system intersecting its boundary enters the interior of the bounded closed domain in the positive direction. Then, Brouwer fixed point theorem is used to prove the existence of crossing periodic solutions and deal with the relationship between periods of the periodic solution and the periods of forced terms.

Key words: bilinear systems, periodic solution, Brouwer fixed point theorem

CLC Number: 

  • O193
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