Abstract. We consider the predator-prey system with a fairly general functional response of Holling type and give a necessary and sufficient condition under which this system has exactly one stable limit cycle. Our result extends previous results and is an answer to a conjecture which was recently presented by Sugie, Miyamoto and Morino.

Our concern is to consider an ecological system with Ivlev's functional response 1 y e ya x of predator to prey. In addition to a, this system contains parameters r and D, which represent the intrinsic rate of increase for the prey population and the death rate for the predator population, respectively. A necessary and sufficient condition for the uniqueness of limit cycles of the predator᎐prey system is Ž . presented. This result gives the bifurcation curve in the a, D -plane. ᮊ 1998 Academic Press

This paper deals with nonautonomous Liénard-type systems. Sufficient conditions are given for the zero solution of the systems to be globally asymptotically stable. The main result is proved by means of phase plane analysis with a Liapunov function. Examples are included to contrast our theorem with results which were presented by Hatvani and Cantarelli. Some global phase portraits are also attached.

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