Research On The Stochastic Dynamics Of Two Types Of Predator-prey Systems With BD Functional Terms

In recent years,environmental pollution has become a problem of close concern in the world.All kinds of pollutants in the environment have a serious impact on the survival of the population,so the study of the impact of environmental pollution on organic organisms has become one of the hot topics in population ecology.However,all species in nature and their mutual relations are a whole,so this paper studies the actual evolution law of the population in the polluted environment based on the most basic predator-prey relationship in the population relationship.In most cases,the more complex ordinary differential equation cannot find the specific analytical solution.And the random factors in real life are everywhere,so the analytical solution of stochastic differential equation cannot be found,only using mathematical software for numerical simulation.In the first chapter,by further improving the random Runge-Kutta method,we give a fourth-order random Runge-Kutta method,and analyze the stability of the method in the mean sense.In real life,any species inevitably suffer from random interference,so the deterministic system cannot effectively demonstrate the real dynamic system and match the real data.In the second chapter,we establish a stochastic predator-prey model with the response of Beddington-De Angelis function in polluted environment.The survival and extinction conditions of each species were analyzed by using the theory of stochastic dynamics.The results show that,compared with the corresponding deterministic system,the long-term dynamic behavior of the population changes significantly under the dual effects of noise and environmental pollution.In addition,the predator population will be significantly reduced and sustained when the prey is subjected to excessive random interference.Finally,we also found that under some conditions,predators and prey populations suffering from random disturbance may be extinct.But in our daily life,toxic substances are often discharged regularly,rather than continuously.Therefore,the continuous toxic emissions cannot simulate the actual situation.In Chapter 3,we establish a stochastic predator-prey model with Beddington-De Angelis in impulsive environment.By using the theory of stochastic dynamics,the conditions of random non average persistence,random weak average persistence,random strong average persistence and extinction of each population are obtained.The results show that,compared with the corresponding stochastic system,the long-term dynamic behavior of the population changes significantly under the dual effects of levy noise and environmental pollution.When the input period of the pulse poison is shortened,the survival state of the population will be changed directly.Finally,the main conclusions are verified by numerical simulation.