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Rational limit cycles of Abel differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2023 We study the number of rational limit cycles of the Abel equation $x'=A(t)x^3+B(t)x^2$, where $A(t)$ and $B(t)$ are real trigonometric polynomials. We show that this number is at most the degree of $A(t)$ plus one.
José Luis Bravo +2 more
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Limit cycles in mass-conserving deficiency-one mass-action systems
Electronic Journal of Qualitative Theory of Differential Equations, 2022 We present some simple mass-action systems with limit cycles that fall under the scope of the Deficiency-One Theorem. All the constructed examples are mass-conserving and their stoichiometric subspace is two-dimensional.
Balázs Boros, Josef Hofbauer
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Maximum number of limit cycles for generalized Liénard polynomial differential systems [PDF]
, 2021 summary:We consider limit cycles of a class of polynomial differential systems of the form $$ \begin {cases} \dot {x}=y, \\ \dot {y}=-x-\varepsilon (g_{21}( x) y^{2\alpha +1} +f_{21}(x) y^{2\beta })-\varepsilon ^{2}(g_{22}( x) y^{2\alpha +1}+f_{22}( x) y^
Bendjeddou, Ahmed +2 more
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Endogenously-Timed Herding And The Synchronization Of Investment Cycles [PDF]
, 2000 This paper combines the recent garne theoretic approach of endogenous timing of entry to herding models with a rnacroeconornic model of investrnent cycles.
Süssmuth, Bernd
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Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four [PDF]
, 2007 summary:A class of degree four differential systems that have an invariant conic $ x^2+Cy^2=1$, $C\in {\mathbb{R}}$, is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under ...
Stange, Eduardo +2 more
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Rational limit cycles of Abel equations [PDF]
, 2021 In this paper we deal with Abel equations dy/dx = A(x)y2 + B(x)y3, where A(x) and B(x) are real polynomials. We prove that these Abel equations can have at most three rational limit cycles and we characterize when this happens.
Valls, Clàudia, Llibre, Jaume
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Synchronization of Coupled Limit Cycles [PDF]
Journal of Nonlinear Science, 2011 Journal of Nonlinear Science ...
openaire +2 more sources
On the approximation of the limit cycles function
Electronic Journal of Qualitative Theory of Differential Equations, 2007 We consider planar vector fields depending on a real parameter. It is assumed that this vector field has a family of limit cycles which can be described by means of the limit cycles function $l$.
L. Cherkas, A. Grin, Klaus Schneider
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Number of limit cycles for planar systems with invariant algebraic curves [PDF]
, 2023 Altres ajuts: acords transformatius de la UABFor planar polynomials systems the existence of an invariant algebraic curve limits the number of limit cycles not contained in this curve.
Gasull, Armengol, Giacomini, Hector
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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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