Results 1 to 10 of about 155,898 (247)
Planar chemical reaction systems with algebraic and non-algebraic limit cycles [PDF]
Journal of Mathematical BiologyThe Hilbert number H(n) is defined as the maximum number of limit cycles of a planar autonomous system of ordinary differential equations (ODEs) with right-hand sides containing polynomials of degree at most n∈N\documentclass[12pt]{minimal} \usepackage ...
Radek Erban +2 more
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The Cubic Polynomial Differential Systems with two Circles as Algebraic Limit Cycles [PDF]
Advanced Nonlinear Studies, 2018 In this paper we characterize all cubic polynomial differential systems in the plane having two circles as invariant algebraic limit cycles.
Giné Jaume, Llibre Jaume, Valls Claudia
doaj +6 more sources
AxiomsIn this paper, two classes of near-Hamiltonian systems with a nilpotent center are considered: the coexistence of algebraic limit cycles and small limit cycles.
Huimei Liu, Meilan Cai, Feng Li
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Algebraic theory of quantum synchronization and limit cycles under dissipation [PDF]
SciPost Physics, 2022 Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop
Berislav Buca, Cameron Booker, Dieter Jaksch
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Polynomial differential systems with hyperbolic algebraic limit cycles
Electronic Journal of Qualitative Theory of Differential Equations, 2020 For a given algebraic curve of degree $n$, we exhibit differential systems of degree greater than or equal $n$, by introducing functions which are solutions of certain partial differential equations.
Salah Benyoucef
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Limit cycles and invariant algebraic curves [PDF]
Communications on Pure and Applied AnalysisWe give lower bounds in terms of~$n,$ for the number of limit cycles of polynomial vector fields of degree~$n,$ having any prescribed invariant algebraic curve. By applying them when the ovals of this curve are also algebraic limit cycles we obtain a new
Paulo Henrique Reis Santana +1 more
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Rational Lyapunov Functions and Stable Algebraic Limit Cycles [PDF]
IEEE Transactions on Automatic Control, 2014 The main goal of this technical note is to show that the class of systems described by a planar differential equation having a rational proper Lyapunov function has asymptotically stable sets which are either locally asymptotically stable equilibrium points, stable algebraic limit cycles or asymptotically stable algebraic graphics. The use of the Zubov
Emmanuel Moulay
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Darboux integrability and algebraic limit cycles for a class of polynomial differential systems [PDF]
Science China Mathematics, 2014 This paper deals with the existence of Darboux first integrals for the planar polynomial differential systems $$\mathop x\limits^. $$ = λx−y+Pn+1(x, y)+xF2n(x, y), $$\mathop y\limits^. $$ = x+λy+Qn+1(x, y)+yF2n(x, y), where Pi(x, y), Qi(x, y) and Fi(x, y)
Xiang Zhang, Jaume Llibre
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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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Algebraic Limit Cycles in Piecewise Linear Differential Systems [PDF]
International Journal of Bifurcation and Chaos, 2018 This paper is devoted to study the algebraic limit cycles of planar piecewise linear differential systems.
C. Buzzi, A. Gasull, Joan Torregrosa
semanticscholar +6 more sources