Population Invasion Model Of Birth And Death Process With Blocking And It's Simulation

In this paper,we are applying stochastic process theory to establish a stochastic mathematical model for study the changed biomass in an ecosystem.By introducing the birth rate with retardation,we find the indicators related to the ecosystem based on the pure process and the birth and death process,and finally computer simulation of the established model to draw conclusions.In the first place,we added a birth rate with a block term from pure birth process.Then using stochastic process theory to find state transition probability and expectation or variance are obtained for population.On this basis,we introduce a death rate and established the model of birth and death and got the probability generator function to determine the population's expectation and variance.There is one more point,through the constructed block and death process model,we consider the composition model of two species i.e.there are native species and alien species in an ecosystem.We established a mathematical model for alien species to invade the local ecosystem according to the Poisson process obeying specific parameters and based on the invasion mechanism to derive the equilibrium equation and solve the state probability and calculate the average survival time and average biomass of the population.The last but not the least,we are simulated the stochastic model by computer.In other words,the entire ecosystem was simulated as a two-dimensional grid plane,and the current biomass and distribution were recorded after an interval(35)t by a more realistic time section method.In addition,we introduce the addition of block term with growth rate of local species gradually slows down with the increase of population biomass which is consistent with the reality.Then,in order to test the rationality and practicability of the model the assumptions of the established model were tested.In the hypothesis test,the effects of the presence or absence of local species on the spatial pattern of local species and alien species were considered respectively.It can be seen from the results that when the local species are added with the retardation term,the change from uniform distribution to aggregation distribution will be delayed,and the alien species will be changed from uniform distribution to aggregation distribution in advance.When invasive species are added the distribution of local species changes from uniform distribution to aggregation distribution in advance,which makes the local species change from uniform distribution to aggregation distribution in advance.The results of this paper have certain theoretical significance for understanding the mechanism of alien species invasion controlling harmful species invasion and formulating local ecosystem protection strategies.