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On the rational limit cycles of Abel equations

Author

Listed:
  • Liu, Changjian
  • Li, Chunhui
  • Wang, Xishun
  • Wu, Junqiao

Abstract

In this paper, we deal with Abel equations: dxdy=A(x)y2+B(x)y3, where A(x) and B(x) are real polynomials. If a solution y=φ(x) of the above equations satisfies that φ(0)=φ(1), then we say that it is a periodic solution. If a periodic solution is isolated, then we call it a limit cycle. If a limit cycle y=φ(x) is a rational function but not a polynomial, then we call it a nontrivial rational limit cycle.

Suggested Citation

  • Liu, Changjian & Li, Chunhui & Wang, Xishun & Wu, Junqiao, 2018. "On the rational limit cycles of Abel equations," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 28-32.
    • Handle: RePEc:eee:chsofr:v:110:y:2018:i:c:p:28-32
    DOI: 10.1016/j.chaos.2018.03.004
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    Cited by:

    1. Llibre, Jaume & Valls, Claudia, 2021. "Phase portraits of the complex Abel polynomial differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Claudia Valls, 2020. "On the Polynomial Solutions and Limit Cycles of Some Generalized Polynomial Ordinary Differential Equations," Mathematics, MDPI, vol. 8(7), pages 1-11, July.
    3. Claudia Valls, 2020. "Rational Limit Cycles on Abel Polynomial Equations," Mathematics, MDPI, vol. 8(6), pages 1-15, June.

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