Dynamic Analysis of Stochastic Spruce Budworm Differential Model with Time Delay

Abstract

In this paper, we consider a stochastic spruce budworm differential model with time delay. Based on the nonnegative initial conditions, the existence and uniqueness of the global positive solution are easily found. Then, we obtain the ultimate boundedness of solution in mean under the same conditions. Furthermore, we verify that the sample Lyapunov exponent of solution is less than a positive constant. Finally, numerical examples are presented to show the consistency of the theoretical results.