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Journal of Applied Mathematics and Stochastic Analysis
Volume 13, Issue 3, Pages 287-297
http://dx.doi.org/10.1155/S1048953300000253

Extinction in a generalized Lotka-Volterra predator-prey model

University of Louisiana at Lafayette, Department of Mathematics, Lafayette, LA 70504-1010, USA

Received 1 September 1998; Revised 1 May 2000

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.