Journal of Applied Mathematics and Stochastic Analysis 
Volume 13 (2000), Issue 3, Pages 287-297
doi:10.1155/S1048953300000253

Extinction in a generalized Lotka-Volterra predator-prey model

Azmy S. Ackleh, David F. Marshall, and Henry E. Heatherly

 University of Louisiana at Lafayette, Department of Mathematics, Lafayette 70504-1010, LA, USA
Received 1 September 1998; Revised 1 May 2000

Abstract

In this paper we discuss the asymptotic behavior of a predator-prey model with distributed growth and mortality rates. We exhibit simple criteria on the parameters which guarantee that all subpopulations but one predator-prey pair are driven to extinction as t→∞. Finally, we present numerical simulations to illustrate the theoretical results.