Stochastic Nicholson-type delay differential system

Abstract

Focusing on Nicholson-type delay differential system in random environments, we introduce the stochastic system to model the dynamics of Nicholson's blowflies population sizes with mortality rates perturbed by white noises. We study the existence and uniqueness of the global positive solution with nonnegative initial conditions. Then the ultimate boundedness in the mean of a solution is derived under the same condition. Moreover, we estimate the sample Lyapunov exponent of the solution, which is less than a positive vector. Finally, an example with its numerical simulations is carried out to support theoretical results.

Keywords:

• Stochastic Nicholson-type delay differential system
• Brownian motion
• ultimate boundedness
• It$\hat{\text{o}}$ formula

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Natural Scientific Research Fund of Zhejiang Province of China (Grant No. LY18A010019), the Natural Science Foundation of Shanghai (Grant No. 17ZR1419900), Shanghai Talent Development Fund (Grant No. 2017128) and ‘Xulun’ Scholar Plan of Shanghai Lixin University of Accounting and Finance.