Boukoucha, Rachid2022-06-132022-06-132017-09-13Boukoucha, R. (2017). Explicit limit cycles of a family of polynomial differential systems. Electronic Journal of Differential Equations, 2017(217), pp. 1-7.1072-6691https://hdl.handle.net/10877/15911We 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.Text7 pages1 file (.pdf)enAttribution 4.0 InternationalPlanar polynomial differential systemFirst integralAlgebraic limit cyclesNon-algebraic limit cycleArticle