A note on "Relaxation Oscillators with Exact Limit Cycles"

Abstract

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.