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Multiple periodic solutions for a discrete time model of plankton allelopathy

Advances in Difference Equations volume 2006, Article number: 090479 (2006) Cite this article

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 and Affiliations

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

    Jianbao Zhang & Hui Fang

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  1. Jianbao Zhang
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  2. Hui Fang
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Correspondence to Jianbao Zhang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zhang, J., Fang, H. Multiple periodic solutions for a discrete time model of plankton allelopathy. Adv Differ Equ 2006, 090479 (2006). https://doi.org/10.1155/ADE/2006/90479

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