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Stochastic Nicholson’s blowflies delayed differential equations. (English) Zbl 1408.34067
Summary: In this paper, we consider a class of stochastic Nicholson’s blowflies delayed differential equations. Firstly, we obtain the existence and uniqueness of the global positive solution with nonnegative initial conditions. Then the ultimate boundedness in mean of solution is derived under the same condition. Moreover, we estimate the sample Lyapunov exponent of the solution, which is less than a positive constant. In the end, an example with its numerical simulations is carried out to validate the analytical results.

MSC:
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
92D25 Population dynamics (general)
60J65 Brownian motion
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