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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
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Algebraic theory of quantum synchronization and limit cycles under dissipation
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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Dulac-Cherkas functions for generalized Liénard systems [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2011 Dulac-Cherkas functions can be used to derive an upper bound for the number of limit cycles of planar autonomous differential systems including criteria for the non-existence of limit cycles, at the same time they provide information about their ...
A. Grin, Klaus Schneider, L. Cherkas
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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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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
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Rational Limit Cycles on Abel Polynomial Equations
Mathematics, 2020 In this paper we deal with Abel equations of the form d y / d x = A 1 ( x ) y + A 2 ( x ) y 2 + A 3 ( x ) y 3 , where A 1 ( x ) , A 2 ( x ) and A 3 ( x ) are real polynomials and A 3 ≢ 0 .
Claudia Valls
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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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Self-oscillations in a certain Belousov–Zhabotinsky model [PDF]
MATEC Web of Conferences, 2022 We consider the dynamic properties of a system of three differential equations known as the oreganator model. This model depends on four external parameters and describes one of the periodic Belousov–Zhabotinsky reactions.
Kondratieva Liudmila, Romanov Aleksandr
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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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Limit Cycles of Polynomially Integrable Piecewise Differential Systems
Axioms, 2023 In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides.
Belén García +3 more
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