The long-time behaviors of non-autonomous stochastic Nicholson’s blowflies systems with patch structure and time delays

Abstract

In this paper, a class of non-autonomous stochastic Nicholson’s blowflies systems with patch structure and time delays is formulated and studied. By constructing suitable Lyapunov functions and using the stochastic technical, the pth moment boundedness and almost sure growth bounds are discussed, which reveal that solutions of the system do not exceed the time value [Formula: see text] and the sample Lyapunov exponent is no more than zero. Then, the system is proved to be exponentially stable (or extinct) if the production rate is less than the mortality rate, which provides an effective reference for the population control. Moreover, taking into account the specific form of time-varying coefficients, related results for several classical stochastic Nicholson’s blowflies systems are studied, and they show the significant improvement of this paper. Finally, numerical simulations for several specific examples are carried out to illustrate our theoretical conclusions.