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Volume 7,     Number 4,     Winter 1999

 

NONEXISTENCE OF LIMIT CYCLES IN
A PREDATOR-PREY SYSTEM WITH A
SIGMOID FUNCTIONAL RESPONSE
M. HESAARAKI AND S.M. MOGHADAS

Abstract. In this paper we consider a predator-prey system with a sigmoid functional response of the form φ(x) = xn/(a+ xn), n > 1. Following Sugie et al. results in [8] and [9], by taking advantage of Freedman and So's theorem in [3], we present a sufficient and necessary condition for the nonexistence of limit cycles of this system with n > 1.

 

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