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The stochastic logistic equation: stationary solutions and their stability. (English) Zbl 1165.60328
Summary: Starting from the logistic equation we introduce uncertainty on the parameters and then we look for stochastic stationary solutions and conditions for their stability. In the stochastic case we do not obtain all the deterministic stationary solutions, but we can find invariant distributions which can be considered the stochastic analogue of the deterministic stationary solutions. In particular, in this work we give conditions on the parameters of the equation under which these invariant distributions exist and conditions under which the stationary solutions are stable.
MSC:
60H10Stochastic ordinary differential equations
60H15Stochastic partial differential equations
93E15Stochastic stability