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Phase portraits of Bernoulli quadratic polynomial differential systems

Electronic Journal of Differential Equations, 2020
In this article we study a new class of quadratic polynomial differential systems. We classify all global phase portraits in the Poincare disk of Bernoulli quadratic polynomial differential systems in R^2.
Jaume Llibre, Weber F. Pereira, Claudio Pessoa   +2 more
doaj   +10 more sources

Abel quadratic differential systems of second kind

Electronic Journal of Differential Equations
The Abel differential equations of second kind, named after Niels Henrik Abel, are a class of ordinary differential equations studied by many authors.
Joan C. Artes, Jaume Llibre, Dana Schlomiuk, Nicolae Vulpe   +3 more
doaj   +6 more sources

Classical planar algebraic curves realizable by quadratic polynomial differential systems [PDF]

International Journal of Bifurcation and Chaos, 2017
In this paper we show planar quadratic polynomial differentialsystems exhibiting as solutions some famous planar invariant algebraic curves. Also we put particular attention to the Darboux integrability of these differential systems.The author is ...
García, I. A. (Isaac A.), Llibre, Jaume
core   +9 more sources

Algebraic limit cycles for quadratic polynomial differential systems [PDF]

Discrete & Continuous Dynamical Systems - B, 2017
We prove that for a quadratic polynomial differential system having three pairs of diametrally opposite equilibrium points at infinity that are positively rationally independent, has at most one algebraic limit cycle.
J. Llibre, C. Valls
semanticscholar   +13 more sources

Quadratic Planar Differential Systems with Algebraic Limit Cycles via Quadratic Plane Cremona Maps [PDF]

Advances in Mathematics, 2019
In this paper we show how we can transform quadratic systems into new quadratic systems after some kind of birational transformations, the quadratic plane Cremona maps.
Maria Alberich-Carramiñana, A. Ferragut, J. Llibre   +2 more
semanticscholar   +10 more sources

Subelliptic Estimates for Overdetermined Systems of Quadratic Differential Operators [PDF]

, 2010
We prove global subelliptic estimates for systems of quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued quadratic symbols.
Pravda-Starov, Karel
core   +6 more sources

On point-dissipative systems of differential equations with quadratic nonlinearity [PDF]

International Journal of Mathematics and Mathematical Sciences, 1991
The system x′=Ax+f(x) of nonlinear vector differential equations, where the nonlinear term f(x) is quadratic with orthogonality property xTf(x)=0 for all x, is point-dissipative if ...
Anile K. Bose, Alan S. Cover, James A. Reneke   +2 more
doaj   +2 more sources

Global configurations of singularities for quadratic differential systems with exactly two finite singularities of total multiplicity four

Electronic Journal of Qualitative Theory of Differential Equations, 2014
In this article we obtain the geometric classification of singularities, finite and infinite, for the three subclasses of quadratic differential systems with $m_f=4$ possessing exactly two finite singularities, namely: (i) systems with two double complex
Joan Artés, Jaume Llibre, Alex Rezende, Dana Schlomiuk, Nicolae Vulpe   +4 more
doaj   +2 more sources

Quadratic differential systems for interactive population models

Journal of Differential Equations, 1969
R. Jenks
semanticscholar   +3 more sources

Bifurcations of the Riccati Quadratic Polynomial Differential Systems [PDF]

International Journal of Bifurcation and Chaos, 2021
In this paper, we characterize the global phase portrait of the Riccati quadratic polynomial differential system [Formula: see text] with [Formula: see text], [Formula: see text] nonzero (otherwise the system is a Bernoulli differential system), [Formula: see text] (otherwise the system is a Liénard differential system), [Formula: see text] a ...
Jaume Llibre, Bruno D. Lopes, Paulo R. da Silva   +2 more
openaire   +5 more sources