Existence of multiple limit cycles in a predator-prey model with arctan(ax) as functional response

We consider a Gause type predator-prey system with functional response given by δ(x) = arctan(ax), where a > 0, and give a counterexample to the criterion given in Attili and Mallak [Commun. Math. Anal. 1:33-40(2006)] for the nonexistence of limit cycles. When this criterion is satisfied, instead this system can have a locally asymptotically stable coexistence equilibrium surrounded by at least two limit cycles.