Dissipativity For Stochastic Species System

Stochastic differential equation in the economic,biological,ecological,and other fields have a wide range of applications.In real life,because there are all kinds of random factors,a stochastic differential equation with perturbation is thus easy to reflect the problem.In the population model in real life,for example,some of the parameters of the mortality and the birth rate is through scientific statistical methods to estimate,however in the statistical re-search population problems are under the given confidence level,through the data confidence interval is calculated,so our population density is also on a range,so the density of popula-tion is also uncertain.Therefore,general stochastic stochastic differential equation is very difficult to describe this sort of question clearly,in order to clear the problem,we joined in the stochastic differential equation fuzzy,Markov jump and some disturbance factors such as environmental noise.But when the population model with these factors,to study their numerical solution is very difficult,this research after joining these factors,the degradation of character of the model.This article mainly discussed under the background of stochas-tic differential equations with random population age related degradation of character of the system.The main content is as follows:The first part,We discussed the age-related fuzzy random population model.Under the condition of bounded(weak in the linear growth condition)and Lipschitz condition,use Ito formula and Bellman-Gronwall-type lemma,establish the fuzzy random population dif-fusion system of age-related mean square dissipation criteria,validated through a numerical example at last.The second part,We discussed with Markov jump time-varying random population har-vesting system numerical solution of the problem.Using the method of Euler-Maruyama analytic solution of the system is given,under the condition of the locally Lipschitz,It is proved that the numerical solution of the equation converges to its analytic solution in the mean square meaning.Finally,the numerical example is verified by numerical examples.The third part,We discussed for a class of fuzzy random under the pollution of the envi-ronment and age related population system,the model takes into account the environmental pollution,the environment noise on the influence of the population,and set the initial value is a fuzzy number.The bounded and Lipschitz condition,use Ito formula and Gronwal-1 lemma,environment pollution is given under the age-related mean square dissipation of fuzzy random population system.