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Página principal > Artículos > Artículos publicados > Bifurcations of the Riccati quadratic polynomial differential systems |
Título variante: | Phase portraits of the Riccati quadratic polynomial differential systems |
Fecha: | 2021 |
Resumen: | In this paper, we characterize the global phase portrait of the Riccati quadratic polynomial differential system ẋ = α2(x), ẏ = ky2 + β1(x)y + γ2(x), with (x,y)∈R2, γ2(x) nonzero (otherwise the system is a Bernoulli differential system), k ≠ 0 (otherwise the system is a Liénard differential system), β1(x) a polynomial of degree at most 1, α2(x) and γ2(x) polynomials of degree at most 2, and the maximum of the degrees of α2(x) and ky2 + β1(x)y + γ2(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 S1 of the infinity) modulo topological equivalence. |
Ayudas: | Agencia Estatal de Investigación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911 European Commission 316338 |
Derechos: | Tots els drets reservats. |
Lengua: | Anglès |
Documento: | Article ; recerca ; Versió acceptada per publicar |
Materia: | Bifurcation ; Topological equivalence ; Riccati system ; Poincaré compactification ; Dynamics at infinity |
Publicado en: | International journal of bifurcation and chaos in applied sciences and engineering, Vol. 31, Issue 6 (May 2021) , art. 2150094, ISSN 1793-6551 |
Postprint 18 p, 835.5 KB |