Results 21 to 30 of about 76,964 (244)
A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems
Expositiones Mathematicae, 2021 In the qualitative theory of differential equations in the plane one of the most difficult objects to study is the existence of limit cycles. There are many papers dedicated to this subject. Here we will present a survey mainly dedicated to the algebraic and explicit non-algebraic limit cycles of the polynomial differential systems in R and of the ...
Llibre, Jaume, Zhang, Xiang
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The 16th Hilbert problem restricted to circular algebraic limit cycles
Journal of Differential Equations, 2016 Agraïments: FEDER-UNAB10-4E-378 and Consolider CSD2007-00004 "ES" We prove the following two results. First every planar polynomial vector field of degree S with S invariant circles is Darboux integrable without limit cycles. Second a planar polynomial vector field of degree S admits at most S - 1 invariant circles which are algebraic limit cycles.
Jaume Llibre +3 more
exaly +9 more sources
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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Algebraic approximations to bifurcation curves of limit cycles for the Lienard equation
Physics Letters A, 1997 In this paper, we study the bifurcation of limit cycles in Lienard systems of the form dot(x)=y-F(x), dot(y)=-x, where F(x) is an odd polynomial that contains, in general, several free parameters.
Giacomini, Hector, Neukirch, Sebastien
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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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Algebraic limit cycles for quadratic polynomial differential systems [PDF]
Discrete & Continuous Dynamical Systems - B, 2018 AbstractAlgebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and a few years later the following conjecture appeared: quadratic polynomial differential systems have at most one algebraic limit cycle. We prove that a quadratic polynomial differential system having an invariant algebraic curve with at most ...
Llibre, Jaume, Valls, Clàudia
+13 more sources
Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
europepmc +2 more sources
Algebraic Limit Cycles Bifurcating from Algebraic Ovals of Quadratic Centers [PDF]
International Journal of Bifurcation and Chaos, 2018 In the integrability of polynomial differential systems it is well known that the invariant algebraic curves play a relevant role. Here we will see that they can also play an important role with respect to limit cycles.In this paper, we study quadratic polynomial systems with an algebraic periodic orbit of degree [Formula: see text] surrounding a ...
Jaume Llibre, Yun Tian
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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. In particular, we present examples exhibiting two explicit hyperbolic algebraic limit cycles, as well as some one-parameter families with a saddle-node bifurcation of algebraic limit cycles.
Claudio A. Buzzi +2 more
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Algebraic limit cycles of planar cubic systems
Sibirskie Elektronnye Matematicheskie Izvestiya, 2020 Algebraic limit cycles of differential systems of the form \[\dot{x}=x+P_3(x,y),\quad \dot{y}=y+Q_3(x,y), \] where \(P_3(x,y)\) and \(Q_3(x,y)\) are homogeneous cubic polynomials, are studied. Note that the results of Theorem 1 were obtained much earlier in the monograph [\textit{V. N. Gorbuzov} and \textit{A. A.
Volokitin, E. P., Cheresiz, V. M.
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