A Study Of Large Properties Of Two Species Competition System

Now the development of interdisciplinary mathematics and ecology is ripe,it has become an important method to study the ecological problems and reveal the laws of ecological phenomena through the establishment of mathematical models, from the Malthus population theory, began to model with the number of single species population,has been to the Lotka-Volterra model, the basic model of predecessors have laid the foundation for future research, and form a pattern: establishing mathematical model,using mathematical method to calculate and simulate, finally, through the calculation results to analyze the biological significance.Most scholars study the competition model,this paper discusses the equilibrium and global stability of the four kinds of different two species competition models, and analyzes their biological significance:The second chapter is the two species competition model with constant input rate,through the calculation, this model has a unique positive equilibrium point, by constructing a ring domain to prove the global asymptotic stability of positive equilibrium point;The third chapter is about the competition model that a population is restricted by density, and a population with constant input rate, after calculation, this model has a unique boundary equilibrium point, calculated and discussed the possible existence of positive equilibrium point, when meet some conditions, this model can have two positive equilibrium points, there can be a positive equilibrium point, even not exist, then by constructing the ring domain to prove the global asymptotic stability of the equilibrium point;The fourth chapter is about the two species are restricted by density of the competition model, is actually the Lotka-Volterra competition model; by calculating shows that there are three boundary equilibrium points, the existence of a positive equilibrium point, by constructing a ring domain to prove the global asymptotic stability of the equilibrium point;The fifth chapter is a population by Allee effect, a population density dependent biological competition model, through the calculation of the model has a unique boundary equilibrium point, calculated and discussed the possible existence of positive equilibrium point, when meet some conditions, this model can have two positive equilibrium points, can also have a positive equilibrium point, even not exist, then by constructing the ring domain to prove the global asymptotic stability of the equilibrium point.