Planar chemical reaction systems with algebraic and non-algebraic limit cycles. [PDF]
J Math BiolAbstract The 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 $$n \in {{\mathbb {N}}}$$ n
Craciun G, Erban R.
europepmc +6 more sources
Explicit non-algebraic limit cycles for polynomial systems
Journal of Computational and Applied Mathematics, 2007 We consider a system of the form x'=P_n(x,y)+xR_m(x,y), y'=Q_n(x,y)+yR_m(x,y), where P_n(x,y), Q_n(x,y) and R_m(x,y) are homogeneous polynomials of degrees n, n and m, respectively, with n<=m. We prove that this system has at most one limit cycle and that when it exists it can be explicitly found.
Armengol Gasull +2 more
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Polynomial differential systems with explicit non-algebraic limit cycles
Electronic Journal of Differential Equations, 2012 Up to now all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree at most 5. Here we show that already there are polynomial differential systems of degree at least exhibiting explicit ...
Rebiha Benterki, Jaume Llibre
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Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems
Electronic Journal of Differential Equations, 2017 In the work by Gine and Grau [11], a planar differential system of degree nine admitting a nested configuration formed by an algebraic and a non-algebraic limit cycles explicitly given was presented.
Ahmed Bendjeddou, Rachid Cheurfa
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A QUINTINC POLYNOMIAL DIFFERENTIAL SYSTEMS WITH EXPLICIT NON-ALGEBRAIC LIMIT CYCLE [PDF]
International Journal of Pure and Applied Mathematics, 2015 R. Boukoucha, A. Bendjeddou
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On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems [PDF]
Mathematica Bohemica, 2023 We study the continuous and discontinuous planar piecewise differential systems separated by a straight line and formed by an arbitrary linear system and a class of quadratic center.
Aziza Berbache
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Application of modelling approaches of twin-screw compressors: thermodynamic investigation and reduced-order model identification [PDF]
E3S Web of Conferences, 2021 Refrigeration is an essential part of the food chain. It is used in all stages of the chain, from industrial food processing to final consumption at home.
Di Mattia Edoardo +3 more
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Non-algebraic limit cycles in Holling type III zooplankton-phytoplankton models [PDF]
Cubo (Temuco), 2021 Summary: 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 are unique for these dynamical systems, are necessarily trascendental ovals.
Homero G. Díaz-Marín, Osvaldo Osuna
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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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Two Non Algebraic Limit Cycles of a Class of Polynomial Differential Systems with Non-Elementary Equilibrium Point [PDF]
Tatra Mountains Mathematical Publications, 2021 Abstract The problems of existence of limit cycles and their numbers are the most difficult problems in the dynamical planar systems. In this paper, we study the limit cycles for a family of polynomial differential systems of degree 6 k + 1, k
Benadouane, Sabah +2 more
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