DYNAMICS OF A FAMILY OF PLANAR DIFFERENTIAL SYSTEMS WITH TWO LIMIT CYCLES EXPLICITLY GIVEN

Abstract

For a given family of planar differential systems it is a very difficult problem to determine its limit cycles. We give a family of planar polynomial differential systems of degree 7 with two limit cycles explicitly given, one of them is an algebraic limit cycles and the other one is a nonalgebraic limit cycles. Concrete examples exhibiting the applicability of our results are introduced.