Results 11 to 20 of about 2,196,572 (258)
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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Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems [PDF]
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 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 0001
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Correction: Number of Limit Cycles for Planar Systems with Invariant Algebraic Curves [PDF]
Qualitative Theory of Dynamical Systems, 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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The 16th Hilbert problem on algebraic limit cycles [PDF]
Journal of Differential Equations, 2011 16.
Xiang Zhang, Zhang, Xiang
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Polynomial differential systems with explicit non-algebraic limit cycles [PDF]
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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A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems [PDF]
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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Algebraic Analysis of Bifurcation and Limit Cycles for Biological Systems [PDF]
, 2008 In this paper, we show how to analyze bifurcation and limit cycles for biological systems by using an algebraic approach based on triangular decomposition, Gröbner bases, discriminant varieties, real solution classification, and quantifier elimination by partial CAD.
Niu, Wei, Wang, Dongming
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On the 16th Hilbert problem for algebraic limit cycles [PDF]
Journal of Differential Equations, 2010 For a polynomial planar vector field of degree n ≥ 2 with generic invariant algebraic curves we show that the maximum number of algebraic limit cycles is 1 + (n − 1)(n − 2)/2 when n is even, and (n − 1)(n − 2)/2 when n is odd. Furthermore, these upper bounds are reached.
Llibre Saló, Jaume +2 more
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Cubic and quartic planar differential systems with exact algebraic limit cycles [PDF]
Electronic Journal of Differential Equations, 2011 We construct cubic and quartic polynomial planar differential systems with exact limit cycles that are ovals of algebraic real curves of degree four. The result obtained for the cubic case generalizes a proposition of [9].
Ahmed Bendjeddou, Rachid Cheurfa
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