Advances in Difference Equations
Volume 2006 (2006), Article ID 90479, 14 pages

Multiple periodic solutions for a discrete time model of plankton allelopathy

Jianbao Zhang and Hui Fang

Center for Nonlinear Science Studies, Kunming University of Science and Technology, Kunming, Yunnan 650093, China

Received 19 May 2005; Revised 25 September 2005; Accepted 27 September 2005

Copyright © 2006 Jianbao Zhang and Hui Fang. 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.


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)N1(k)a22(k)N2(k)b2(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.