Global phase portraits of some reversible cubic centers with noncollinear singularities

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The results in this paper show that the cubic vector fields = -y + M(x, y) - y(x2 + y2), = x + N(x, y) + x( x2 + y 2), where M, N are quadratic homogeneous polynomials, having simultaneously a center at the origin and at infinity, have at least 61 and at most 68 topologically different phase portraits. To this end, the reversible subfamily defined by M(x, y) = -γxy, N(x, y) = (γ - λ)x 2 + α2λy2 with α, γ ∈ ℝ and λ ≠ 0, is studied in detail and it is shown to have at least 48 and at most 55 topologically different phase portraits. In particular, there are exactly five for γλ < 0 and at least 46 for γλ > 0. Furthermore, the global bifurcation diagram is analyzed.

Idioma originalEnglish
Número d’article1350161
RevistaInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volum23
Número9
DOIs
Estat de la publicacióPublicada - de set. 2013

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