Bifurcations of the Riccati Quadratic Polynomial Differential Systems

Jaume Llibre, Bruno D. Lopes, Paulo R. Da Silva

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1 Citation (Scopus)


In this paper, we characterize the global phase portrait of the Riccati quadratic polynomial differential system ? = a2(x), = ky2 + ß 1(x)y + ?2(x), with (x,y) 2, ?2(x) nonzero (otherwise the system is a Bernoulli differential system), k0 (otherwise the system is a Liénard differential system), ß1(x) a polynomial of degree at most 1, a2(x) and ?2(x) polynomials of degree at most 2, and the maximum of the degrees of a2(x) and ky2 + ß 1(x)y + ?2(x) is 2. We give the complete description of the phase portraits in the Poincaré disk (i.e. in the compactification of R2 adding the circle 1 of the infinity) modulo topological equivalence.

Original languageEnglish
Article number2150094
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number6
Publication statusPublished - May 2021


  • Bifurcation
  • Poincaré compactification
  • Riccati system
  • dynamics at infinity
  • topological equivalence


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