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Integrability of planar polynomial differential systems through linear differential equations [PDF]
Rocky Mountain Journal of Mathematics, 2005 In this work, we consider rational ordinary differential equations dy/dx = Q(x,y)/P(x,y), with Q(x,y) and P(x,y) coprime polynomials with real coefficients.
Giacomini, Héctor +2 more
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Limit Cycles of Polynomially Integrable Piecewise Differential Systems
Axioms, 2023 In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides.
Belén García +3 more
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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 +2 more
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Journal of High Energy Physics, 2018 The formal derivatives of the Yang-Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differential equations.
R. S. Vieira
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Rigid Polynomial Differential Systems with Homogeneous Nonlinearities
MathematicsPlanar differential systems whose angular velocity is constant are called rigid or uniform differential systems. The first rigid system goes back to the pendulum clock of Christiaan Huygens in 1656; since then, the interest for the rigid systems has been
Jaume Llibre
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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 +2 more
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Algebraic limit cycles for quadratic polynomial differential systems [PDF]
Discrete & Continuous Dynamical Systems - B, 2018 AbstractAlgebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and a few years later the following conjecture appeared: quadratic polynomial differential systems have at most one algebraic limit cycle. We prove that a quadratic polynomial differential system having an invariant algebraic curve with at most ...
Llibre, Jaume, Valls, Clàudia
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Dynamics of the polynomial differential systems
Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2023 In general, there are several free parameters. By using a method introduced in a previous paper, we obtain a sequence of algebraic a proximations to the bifurcationsets,in the parameter ...
Feneniche Fatima, Rezaoui Med Salem
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Polynomial and rational first integrals for planar homogeneous polynomial differential systems [PDF]
Publicacions Matemàtiques, 2021 In this paper we find necessary and suficient conditions in order that a planar homogeneous polynomial differential system has a polynomial or rational first integral. We apply these conditions to linear and quadratic homogeneous polynomial differential systems.
Giné, Jaume, Grau, Maite, Llibre, Jaume
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Fifteen Limit Cycles Bifurcating from a Perturbed Cubic Center
Discrete Dynamics in Nature and Society, 2021 In this work, we study the bifurcation of limit cycles from the period annulus surrounding the origin of a class of cubic polynomial differential systems; when they are perturbed inside the class of all polynomial differential systems of degree six, we ...
Amor Menaceur +3 more
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