Results 1 to 10 of about 43 (42)
Invariant Algebraic Curves of Generalized Liénard Polynomial Differential Systems
Mathematics, 2022 In this study, we focus on invariant algebraic curves of generalized Liénard polynomial differential systems x′=y, y′=−fm(x)y−gn(x), where the degrees of the polynomials f and g are m and n, respectively, and we correct some results previously stated.
Jaume Giné, Jaume Llibre
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On Control Polygons of Planar Sextic Pythagorean Hodograph Curves
Mathematics, 2023 In this paper, we analyze planar parametric sextic curves to determine conditions for Pythagorean hodograph (PH) curves. By expressing the curves to be analyzed in the complex form, the analysis is conducted in algebraic form.
Yujun Li +3 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2021 During the last forty years the theory of integrability of Darboux, in terms of algebraic invariant curves of polynomial systems has been very much extended and it is now an active area of research.
Regilene Oliveira +3 more
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Acta et Commentationes: Ştiinţe Exacte şi ale Naturii, 2023 In this paper for a cubic differential system with a singular point
Dumitru Cozma
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Non-algebraic limit cycles in Holling type III zooplankton-phytoplankton models
Cubo, 2021 We prove that for certain polynomial differential equations in the plane arising from predator-prey type III models with generalized rational functional response, any algebraic solution should be a rational function. As a consequence, limit cycles, which
Homero G. Díaz-Marín, Osvaldo Osuna
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On a class of invariant algebraic curves for Kukles systems
Electronic Journal of Qualitative Theory of Differential Equations, 2016 In this paper we give a new upper bound for the degree of a class of transversal to infinity invariant algebraic curves for polynomial Kukles systems of arbitrary degree.
Osvaldo Osuna +2 more
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Characteristic Number: Theory and Its Application to Shape Analysis
Axioms, 2014 Geometric invariants are important for shape recognition and matching. Existing invariants in projective geometry are typically defined on the limited number (e.g., five for the classical cross-ratio) of collinear planar points and also lack the ability ...
Xin Fan +5 more
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Quadratic systems with a symmetrical solution
Electronic Journal of Qualitative Theory of Differential Equations, 2018 In this paper we study the existence and uniqueness of limit cycles for so-called quadratic systems with a symmetrical solution: \begin{equation*} \begin{split} \frac{dx(t)}{dt}& = P_2(x,y) \equiv a_{00}+a_{10}x+a_{01}y+a_{20}x^2+a_{11}xy+a_{02}y^2 ...
Andre Zegeling, Robert Kooij
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The Ceresa class and tropical curves of hyperelliptic type
Forum of Mathematics, SigmaWe define a new algebraic invariant of a graph G called the Ceresa–Zharkov class and show that it is trivial if and only if G is of hyperelliptic type, equivalently, G does not have as a minor the complete graph on four vertices or the loop of three ...
Daniel Corey, Wanlin Li
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Electronic Journal of Qualitative Theory of Differential EquationsConsider the class ${\bf QS}$ of all non-degenerate planar quadratic differential systems and its subclass ${\bf QSP}$ of all its systems possessing an invariant parabola.
Nicolae Vulpe
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