Research On The Stability Of Random Biological Models And Their Numerical Simulatio

We live in a real world closely related to biological systems.Understanding the dynamic behaviors and properties of stochastic biological systems,and using theoretical knowledge and technology to fully simulate the living conditions that biological systems meet are of great significance and value for the development of society and the management of nature.We study two biological models,one is the random predatorprey ecosystem,and the other is the stochastic age-structured population model.The specific research content is as follows:Firstly,we focus on the mean-square stability of the stochastic ratio-dependent predator-prey model.In order to measure the response to external perturbations and analyze the mean-square stability of this system,we calculate the root-mean-square resilience,root-mean-square reactivity and root-mean-square envelope amplification of the interior equilibrium by using the mean-square stable matrix.The main tools used in this chapter are Kronecker product and numerical simulation,and the main conclusions are obtained.As the disturbance intensity increases,the root-mean-square resilience decreases,the root-mean-square reactivity increases,and the root-mean-square amplification envelope increases.The above changes imply that the mean-square stable area reduces,and mean-square stability of the system becomes weaker.After that,we studied a kind of stochastic age-structured population model.Based on the biological characteristics,we discussed the positivity of the numerical solution for this model,and constructed a new numerical scheme that can keep the numerical solution positive.The main methods include the explicit Euler method and the Balanced Implicit method.Then,we analyzed the convergence of this positivity preserving numerical scheme,and calculated that its strong convergence order is 1/2.Finally,two examples are given to verify the accuracy of the conclusions.