Abstract
Discrete model of plankton allelopathy is studied. The model allows for a fluctuating environment. Sufficient conditions, which guarantee the permanence of the model are obtained at first. Assuming that the coefficients in the model are periodic, the existence of periodic solutions are also obtained. At last, by linearization of the model at positive periodic solutions and construction of Lyapunov function, sufficient conditions are obtained to ensure the global stability of the positive periodic solution.
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