Explicit limit cycles of a family of polynomial differential systems
Date
2017-09-13
Authors
Boukoucha, Rachid
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider the family of polynomial differential systems
x' = x + (αy - βx) (αx2 - bxy + αy2)n,
y' = y - (βy + αx) (αx2 - bxy + αy2)n,
where α, b, ɑ, β are real constants and n is positive integer. We prove that these systems are Liouville integrable. Moreover, we determine sufficient conditions for the existence of an explicit algebraic or non-algebraic limit cycle. Examples exhibiting the applicability of our result are introduced.
Description
Keywords
Planar polynomial differential system, First integral, Algebraic limit cycles, Non-algebraic limit cycle
Citation
Boukoucha, R. (2017). Explicit limit cycles of a family of polynomial differential systems. Electronic Journal of Differential Equations, 2017(217), pp. 1-7.
Rights
Attribution 4.0 International