Dynamic behaviors of a delay differential equation model of plankton allelopathy |
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Authors: | Fengde Chen,Zhong Li,Xiaoxing Chen,Jitka Laitochová |
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Affiliation: | 1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, PR China;2. Department of Mathematics, Faculty of Education, Palacký University, Olomouc, Czech Republic |
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Abstract: | In this paper, we consider a modified delay differential equation model of the growth of n-species of plankton having competitive and allelopathic effects on each other. We first obtain the sufficient conditions which guarantee the permanence of the system. As a corollary, for periodic case, we obtain a set of delay-dependent condition which ensures the existence of at least one positive periodic solution of the system. After that, by means of a suitable Lyapunov functional, sufficient conditions are derived for the global attractivity of the system. For the two-dimensional case, under some suitable assumptions, we prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation. Examples show the feasibility of the main results. |
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Keywords: | 34C25 92D25 34D20 34D40 |
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