Study On The Stability For A Class Of Stochastic Nicholson’s Blowflies Models

The stochastic Nicholson’s blowflies model is an important and representative population model.The existence and stability of the almost periodic solution for the stochastic Nicholson’s blowflies model are important dynamic properties.On the other hand,it is generally difficult to find the specific expression of the solution of the model.For the needs of practical applications,numerical solutions are usually used to approximate analytical solutions.Therefore,it is necessary to develop and apply corresponding numerical methods to study the dynamic behavior of stochastic population models.In this thesis,we mainly study the existence and stability of the almost periodic solution for a kind of semi-discrete stochastic Nicholson’s blowflies model,and the stability of the model based on the θ-Heun method from the perspective of qualitative analysis and numerical method,respectively.First,we establish a semi-discrete stochastic Nicholson’s blowflies model by utilizing the semi-discrete technique.With the help of Minkowski inequality,H?lder inequality,Krasnoselskii fixed point theorem and so on,we give some sufficient conditions that guarantee the existence and stability exponential of the almost periodic sequence solution for the model.On this basis,we verify the rationality and effectiveness of the theory through numerical simulation.Furthermore,when the daily mortality αi(t)of adults and the time delay Tij(t)are constants,we obtain the sufficient conditions ensuring the mean-square exponential stability and almost everywhere exponential stability of the model by use of the θ-Heun method.In the end,we also verify the rationality and feasibility of the theoretical results by numerical experiments.Our results show that under certain conditions,the model is stable from both qualitative and numerical perspectives.