Results 231 to 240 of about 76,964 (244)

NON-ALGEBRAIC LIMIT CYCLES FOR PARAMETRIZED PLANAR POLYNOMIAL SYSTEMS

International Journal of Mathematics, 2007
In this paper, we determine conditions for planar systems of the form [Formula: see text] where a, b and c are real constants, to possess non-algebraic limit cycles. This is done as an application of a former theorem gives description of the existence of the non-algebraic limit cycles of the family of systems: [Formula: see text] where Pn(x,y), Qn(x,y)
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Algebraic limit cycles in polynomial systems of differential equations

Journal of Physics A: Mathematical and Theoretical, 2007
Using elementary tools we construct cubic polynomial systems of differential equations with algebraic limit cycles of degrees 4, 5 and 6. We also construct a cubic polynomial system of differential equations having an algebraic homoclinic loop of degree 3. Moreover, we show that there are polynomial systems of differential equations of arbitrary degree
Jaume Llibre, Yulin Zhao
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Algebraic Limit Cycles

International Journal of Bifurcation and Chaos
In the qualitative theory of differential equations in the plane [Formula: see text], one of the most difficult objects to study is the existence of limit cycles. Here, we summarize some results and open problems on the algebraic limit cycles of the planar polynomial differential systems.
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Coexistence of algebraic and non-algebraic limit cycles, explicitly given, using Riccati equations

Nonlinearity, 2006
We give a family of planar polynomial differential systems whose limit cycles can be explicitly described using polar coordinates. Moreover, we characterize the multiplicity of each one of the limit cycles whenever they exist. The given family of planar polynomial differential systems can have at most two limit cycles, counted with multiplicity.As an ...
Jaume Giné, Maite Grau
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Coexistence of algebraic and nonalgebraic limit cycles in Kukles systems

Periodica Mathematica Hungarica, 2008
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Sáez, Eduardo, Szántó, Iván
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Algebraical Limit Cycles of Polynomial Vector Fields on the Plane

Differential Equations, 2001
The existence of limit cycles of algebraic differential equations has been studied and their number has been estimated in numerous papers. In recent decades, much attention was paid to polynomial vector fields with invariant algebraic curves. The statement of the problem goes back to Darboux, Poincaré, and Erugin.
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Lie algebras and dynamic nonlinear systems containing limit cycles

International Journal of Theoretical Physics, 1977
Certain Lie algebras, represented as linear partial differential operators of first order, are used to derive autonomous systems of differential equations which involve limit cycles. To illustrate the approach an example is given.
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Homology for operator algebras. IV. On the regular classification of limits of 4-cycle algebras

1997
According with the terminology and notations from the research notes ``Limit algebras'' [Pitman Research Notes in Math. 278, London (1993)] of the second author, the subject of the present paper is related to the 4-cycle algebras, that is a CSL-algebra whose reduced digraph is a 4-cycle, and to the regular direct systems of 4-cycle algebras with rigid ...
Power, Stephen C., Donsig, A. P.
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Relationships between limit cycles and algebraic invariant curves for quadratic systems

Journal of Differential Equations, 2006
Jaume Llibre, Grzegorz Swirszcz
exaly  

Planar polynomial vector fields having first integrals and algebraic limit cycles

Journal of Mathematical Analysis and Applications, 2010
Hai-xia Jiang
exaly