Abstract
In this paper, we introduce a multi-parameter quintinc polynomial differential system for which we prove the existence of a non-algebraic limit cy- cle. Moreover this limit cycle is explicitely given in polar coordinates. Concrete examples exhibiting the applicability of our result are introduced.
Highlights
An important problem of the qualitative theory of differential equations is to determine the limit cycles of a system of the form x′ = P (x, y) y′ = Q(x, y) where P (x, y) and Q(x, y) are coprime polynomials and we denote by n = max {deg P, deg Q} and we say that n is the degree of system 1.1, see [5]
We introduce a multi-parameter quintinc polynomial differential system of the form x′ = x (m + l) x2 + 2nxy + (m − l) y2
The multi-parameter polynomial differential system 1.2, has non-algebraic limit cycle explicitly given in polar coordinates (r, θ) by : r (θ)
Summary
In [1, 6], and [7] examples of explicit limit cycles which are not algebraic are given.
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