Results 11 to 20 of about 8,933,474 (280)
Global phase portraits of the generalized van der Pol systems [PDF]
Bulletin des Sciences Mathématiques, 2023 We consider the generalized van der Pol systems x˙ = y, y˙ = -x + (1-x) f(y), where f ∈ R[y]. The classical van der Pol systems have f(y) = y. We first characterize when the origin of the generalized van der Pol systems is a center, and second we provide the global phase portraits in the Poincaré disc of the generalized van der Pol when f(y) = ay + ay ...
Jaume Llibre, Claudia Valls
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Global Phase Portraits for the Kukles Systems of Degree 3 with ℤ2-Reversible Symmetries
International Journal of Bifurcation and Chaos, 2021 We provide the normal forms, the bifurcation diagrams and the global phase portraits on the Poincaré disk of all planar Kukles systems of degree [Formula: see text] with [Formula: see text]-symmetries.
Fabio Scalco Dias +2 more
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Phase portraits of Bernoulli quadratic polynomial differential systems [PDF]
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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GLOBAL PHASE PORTRAITS OF QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS WITH A SEMI-ELEMENTAL TRIPLE NODE [PDF]
International Journal of Bifurcation and Chaos, 2013 Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family.
Joan C. Artés +2 more
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Global Phase Portraits of Quadratic Systems with a Complex Ellipse as Invariant Algebraic Curve [PDF]
Acta Mathematica Sinica, English Series, 2017 In this paper we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex ellipse x^2 y^2 1=0 as invariant algebraic curve.
Llibre, Jaume, Valls, Clàudia
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Global Phase Portrait and Local Integrability of Holomorphic Systems
Qualitative Theory of Dynamical Systems, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gouveia, Luiz F. S. +2 more
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A class of nonlinear oscillators with non-autonomous first integrals and algebraic limit cycles
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we present a class of autonomous nonlinear oscillators with non-autonomous first integral. We prove explicitly the existence of a global sink which is, under some conditions, an algebraic limit cycle.
Meryem Belattar +3 more
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Global phase portraits of the key pitchfork bifurcation [PDF]
SCIENTIA SINICA Mathematica, 2019 This paper deals with the following quadratic polynomial differential system$\frac{dx}{dt}=y^{2}-y-x,$ $\frac{dy}{dt}=x^{2}$ $-\,~\mu~x-y,$with parameter $\mu\in\mathbb{R}$, which is the key example for studying the pitchfork bifurcation of a singular point. We classify the global phase portraits in the Poincare disc of this system when $\mu$ varies.
Jaume, Llibre, Shimin, Li
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Darboux polynomials and global phase portraits for the D2 vector field [PDF]
Journal of Mathematical Analysis and Applications, 2019 We study a vector field of R^3 equivariant under the D_2 symmetry group, called "the D_2 field" in the literature. We construct the complete list of Darboux polynomials for it, solving the partial differential equation defining them. We also use these polynomials to comment on its global qualitative behaviour.
Katsios, Kostas, Anastassiou, Stavros
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Global Portraits of Nonminimal Teleparallel Inflation
Universe, 2021 We construct global phase portraits of inflationary dynamics in teleparallel gravity models with a scalar field nonminimally coupled to torsion scalar.
Laur Järv, Joosep Lember
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