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A stochastic chemostat model with periodic washout rate is proposed in this paper. First, sufficient conditions are established for the existence of stochastic nontrivial positive periodic solution for the system, on the basis of Khasminskii’s theory for periodic Markov processes. Furthermore, we observe that there exists a unique boundary periodic solution of the stochastic model which is globally...
The paper characterizes some qualitative dynamic properties of a stochastic non-autonomous multi-species mutualism model, with continuous periodic parameters. Using Khasminskii theory of stability with suitable Lyapunov functions, and M-Matrices, sufficient conditions are established to guarantee existence of positive periodic solutions to the system. We also provide conditions for the global attractiveness...
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