Limit cycles in Kukles systems of arbitrary degree with invariant ellipse Original Research Article

In this paper a normal form is obtained for the Kukles polynomial systems of arbitrary degree with an invariant ellipse. We study some existence and uniqueness results for limit cycles of that family. Moreover, the tangential sixteenth Hilbert problem is discussed for those polynomial systems showing an upper bound for the number of bifurcated limit cycles depending on the degree of the system. We conclude with some numerical simulations of the results obtained.