The Solution For A Class Of Nonlinear Population Dynamics With Migration Perturbations

With the development of science, sociology and population problems have always been closely linked and being considered as a pure social science aspect. But now with the achievements of scientific and technological, the population problem has not been the only subject of social science studies. When it combines with modern mathematics achievement, we can see more clearly of the population and substance. Population change is determined by many factors in a society. However, birth, death and migration of residents are the direct cause of population changes. All the factors on the number of the population are affected by the phenomenon. If we could establish the relation, we can get a population equation model. Investigated the population of a stable social groups, theoretical analysis and the actual statistics indicate that population changes has something with time and age's continuous changes. These are the most direct reasons that effect both births and deaths, so we can use a partial differential equation to describe it. Considering the environment, employment conditions, too much population is linked to the total population. The population model is an extensive population issues partial differential equation model. It is Malthusian population model and the further promotion of Verhulst model. So to research on population issues is to study such problems.This paper has three parts. Chapterâ… :Introduction on the background of the population equation. Chapterâ…¡:Preliminary. We introduced the concept and nature of population function, the nature of the series and integral variables points. Chapterâ…¢:Focuses on the derivation of the model. Taking into account of mortality have something with the total population, and the immigrant population model. In the conditions of the certain initial boundary value, assuming zero order compatible conditions and a first band compatible conditions are established, we adopt appropriate transformation and gradually approximation method to solve the problem. We deduce the expressions and properties of the solutions, and prove the existence and uniqueness of solutions. The population density function we get reflect the regular of population development process as the changes of ages and time, so that we could control the population development process more accurately.