Open Access

Multiple periodic solutions for a discrete time model of plankton allelopathy

Advances in Difference Equations20062006:090479

DOI: 10.1155/ADE/2006/90479

Received: 19 May 2005

Accepted: 27 September 2005

Published: 23 February 2006

Abstract

We study a discrete time model of the growth of two species of plankton with competitive and allelopathic effects on each other N1(k+1) = N1(k)exp{r1(k)-a11(k)N1(k)-a12(k)N2(k)-b1(k)N1(k)N2(k)}, N2(k+1) = N2(k)exp{r2(k)-a21(k)N2(k)-b2(k)N1(k)N1(k)N2(k)}. A set of sufficient conditions is obtained for the existence of multiple positive periodic solutions for this model. The approach is based on Mawhin's continuation theorem of coincidence degree theory as well as some a priori estimates. Some new results are obtained.

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Authors’ Affiliations

(1)
Center for Nonlinear Science Studies, Kunming University of Science and Technology

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Copyright

© J. Zhang and H. Fang 2006

This article is published under license to BioMed Central Ltd. 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.