A note on "Relaxation Oscillators with Exact Limit Cycles"

In this note we give a family of planar polynomial differential systems with a prescribed hyperbolic limit cycle. This family constitutes a corrected and wider version of an example given in the work of M.A. Abdelkader entitled ``Relaxation Oscillators with Exact Limit Cycles’', which appeared in J. Math. Anal. Appl. 218 (1998), 308–312. The result given in this note may be used to construct models of Li'enard differential equations exhibiting a desired limit cycle.