Analysis And Numerical Simulation Of Environmental Pollution Logistics Population Growth System?

Nowadays,human social production activities have caused complex ecological environment pollution problems.Environmental pollution is not conducive to the development and reproduction of biological populations,and has a crucial impact on the distribution of organisms in nature.Therefore,it is of great significance to study the impact of pollution emission rates on the changes in the number of individuals in a single population.This dissertation is based on the background of environmental pollution to study the survival of biological groups.That is,the threshold value of biological extinction or continuous survival is determined by the pollution discharge rate through the model,in the polluted environment,the threshold value of population persistence or extinction is determined by the species pair.It is determined by the reflection intensity of the toxin,the intrinsic growth rate of the biological population,and the average toxin concentration in the individual population.First,we clarified the significance of the improvement of the It (?)-type Logistic model in a polluted environment.White noise was used to randomly interfere with the biological intrinsic growth rate,the in vivo toxin concentration of biological individuals,and the environmental toxin concentration,and the pollution The stochastic logistic model in the environment is improved to the It (?) logistic model.In the theoretical research part,use the It (?) formula to verify the explicit solution of the equations in the model,and then study some properties of the environmental toxin concentration CE(t)and the biological concentration C0(t).Finally,use the properties of Brownian motion,the strong law of numbers of local martingales and random comparisons Theorem and other methods,deal with the explicit solution of the number of biological populations x(t),and obtain the threshold value of the system control function toxin emission rate u(t)that makes the population tend to random persistence,random weak average persistence and local extinction.Secondly,according to the theoretic conditions of population local extinction,random weak average persistence and random persistence in this dissertation,appropriate parameters are selected to carry out numerical simulation of the It (?)-type Logistic model M.The model M is combined with only considering the influence of noise on the intrinsic growth model M2.The comparison results show that while keeping the growth rate,absorption rate and purification rate unchanged,random disturbance to the absorption rate k and purification rate h is beneficial to the survival of organisms in a polluted environment.After considering the noise interference,the numerical simulation results of the model are more in line with the change law of the number of species.At the end of the dissertation,we discuss the rationality and feasibility of using the fractional Brownian motion of colored noise as random disturbances.At the same time,as a related basic research,we establish the limit theorem for a class of integral functionals of fractional Brownian motion.