Characterization of the Existence of Non-trivial Limit Cycles for Generalized Abel Equations

Abstract

In this paper, we consider the family of generalized Abel equations of the form

$$\begin{aligned} x'=A(t)x^m + B(t) x^n, \end{aligned}$$

where AB are trigonometric polynomials and \(m,n\in \mathbb {N}\). We characterize the existence of non-trivial limit cycles in this family, in terms of the trigonometric monomials.

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Correspondence to M. J. Álvarez.

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The four authors are partially supported by MINECO/FEDER Grant No. MTM2017-83568-P. J.L.B. and M.F. are also partially supported by the Junta de Extremadura/FEDER Grant Nos. GR18023 and IB18023.

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Álvarez, M.J., Bravo, J.L., Fernández, M. et al. Characterization of the Existence of Non-trivial Limit Cycles for Generalized Abel Equations. Qual. Theory Dyn. Syst. 20, 15 (2021). https://doi.org/10.1007/s12346-021-00450-4

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Keywords

  • Limit cycles
  • Periodic orbits
  • Abel equation

Mathematics Subject Classification

  • 34C25