Results 1 to 10 of about 95,578 (255)
Invariant Algebraic Curves of Generalized Liénard Polynomial Differential Systems [PDF]
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
doaj +7 more sources
On the algebraic invariant curves of plane polynomial differential systems [PDF]
Journal of Physics A: Mathematical and General, 2000 We consider a plane polynomial vector field $P(x,y)dx+Q(x,y)dy$ of degree $m>1$. To each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential $\omega=dx/P=dy/Q$. The asymptotic estimate of the
Alexei Tsygvintsev +12 more
core +7 more sources
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
doaj +5 more sources
Inverse problems for invariant algebraic curves : explicit computations [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2007 Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant.
Cristopher, Colin +4 more
core +6 more sources
Chaos and bifurcations of a discretized Holling-II prey-predator model including prey refuge and Allee effect [PDF]
Scientific ReportsThis study examines the dynamics of a discrete-time predator-prey system incorporating a Holling Type-II functional response, the Allee effect, and a refuge term. Through algebraic analysis, we establish the occurrence of Period-Doubling (PD) and Neimark-
Md. Mutakabbir Khan, Md. Jasim Uddin
doaj +2 more sources
Necessary and sufficient conditions for the existence of invariant algebraic curves
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We present a set of conditions enabling a polynomial system of ordinary differential equations in the plane to have invariant algebraic curves. These conditions are necessary and sufficient. Our main tools include factorizations over the field of Puiseux
Maria Demina
doaj +1 more source
A linking invariant for algebraic curves [PDF]
L’Enseignement Mathématique, 2020 We construct a topological invariant of algebraic plane curves, which is in some sense an adaptation of the linking number of knot theory. This invariant is shown to be a generalization of the \mathcal I -invariant of line arrangements developed by ...
Guerville-Ballé, Benoît +1 more
openaire +5 more sources
The algebraic curves of planar polynomial differential systems with homogeneous nonlinearities
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We consider planar polynomial systems of ordinary differential equations of the form $\dot x = x + P_n(x,y)$, $\dot y = y + Q_n(x,y)$, where $P_n(x,y),\ Q_n(x,y)$ are homogeneous polynomials of degree $n$.
Vladimir Cheresiz, Evgenii Volokitin
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source