Discrete Dynamics in Nature and Society 
Volume 2006 (2006), Article ID 64590, 13 pages
doi:10.1155/DDNS/2006/64590

Stability analysis of stochastic Ricker population model

Natali Hritonenko,1 Alexandra Rodkina,2 and Yuri Yatsenko3

 1Department of Mathematics, Prairie View A & M University, P.O. Box 4189, Prairie View 77446, TX, USA
2Department of Mathematics and Computer Science, University of the West Indies, Mona, Kingston 7, Jamaica
3College of Business and Economics, Houston Baptist University, 7502 Fondren Road, Houston 77074, TX, USA
Received 10 October 2005; Accepted 19 December 2005

Abstract

A stochastic generalization of the Ricker discrete population model is studied under the assumption that noise impacts the population reproduction rate. The obtained results demonstrate that the demographic-type stochastic noise increases the risk of the population extinction. In particular, the paper establishes conditions on the noise intensity under which the population will extinct even if the corresponding population with no noise survives.