Non-algebraic limit cycle - Open Access .click

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
Meryem Belattar, Rachid Cheurfa, Ahmed Bendjeddou +2 more
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

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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first integral
algebraic limit cycle
qa1-939

polynomial vector field
non-algebraic solution
polynomial planar system

poincare return-map
limit cycle
mathematics