Results 191 to 200 of about 12,856,242 (214)

On a Liouville Integrable Planar Differential System with Non-Algebraic Limit Cycle

2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI), 2021
In this paper, we prove that a class of differential system of degree nine is Liouville integrable by transforming it into a Bernoulli differential equation and we determine exactly its first integral. This allows us to show that this class admits an explicit non-algebraic limit cycle enclosing the origin, here a non-elementary singular point.
Ahmed Bendjeddou
exaly   +2 more sources

Cubic planar differential systems with non-algebraic limit cycles enclosing a focus

International Journal of Dynamical Systems and Differential Equations, 2023
Ahmed Bendjeddou
exaly   +2 more sources

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.
Armengol Gasull
exaly   +2 more sources

Classification of quadratic systems admitting the existence of an algebraic limit cycle [PDF]

Bulletin Des Sciences Mathematiques, 2007
In the paper we find a set of necessary conditions that must be satisfied by a quadratic system in order to have an algebraic limit cycle. We find a countable set of ⩽5 parameter families of quadratic systems such that every quadratic system with an ...
Jaume Llibre, Grzegorz Świrszcz
exaly   +2 more sources

Uniqueness of Algebraic Limit Cycles for Quadratic Systems [PDF]

Journal of Mathematical Analysis and Applications, 2001
We know five different families of algebraic limit cycles in quadratic systems, one of degree 2 and four of degree 4. Moreover, if there are other families of algebraic limit cycles for quadratic systems, then their degrees must be larger than 4.
Jaume Llibre, Hector Giacomini
exaly   +2 more sources

Planar Polynomial Systems with Non-Algebraic Limit Cycles

AIP Conference Proceedings, 2009
In this paper, we study the existence of the non‐algebraic limit cycles of the systems dxdt = Pn(x,y)+xRm(x,y) dydt = Qn(x,y)+yRm(x,y) where Pn(x,y), Qn(x,y) and Rm(x,y) are homogeneous polynomials of degrees n, n and m respectively with ...
Khalil I. T. Al-Dosary, George Maroulis, Theodore E. Simos   +2 more
openaire   +1 more source

Algebraic limit cycles of degree 4 for quadratic systems [PDF]

Journal of Differential Equations, 2004
Yablonskii (Differential Equations 2 (1996) 335) and Filipstov (Differential Equations 9 (1973) 983) proved the existence of two different families of algebraic limit cycles of degree 4 in the class of quadratic systems. It was an open problem to know if
Jaume Llibre
exaly   +2 more sources

Algebraic limit cycles for quadratic polynomial differential systems [PDF]

Discrete and Continuous Dynamical Systems - Series B, 2018
We prove that for a quadratic polynomial differential system having three pairs of diametrally opposite equilibrium points at infinity that are positively rationally independent, has at most one algebraic limit cycle.
Claudia Valls, Jaume Llibre
exaly   +2 more sources

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)
openaire   +2 more sources