A Dynamical System Model In The Social Security

Mathematic model is a mathematic structure, which focus on a particular object in real world. In order to get a special purpose, and in accordance with its internal rules, it was simplified and made some necessary assumptions through the use of appropriate mathematical tools. It can explain the state of certain phenomena in reality, or can predict the future state of the object, or it can provide the optimal treatment decision-making or control. In this essay, mathematic model was used as a tool to study the problem of social order and social stability, and some mathematical methods was used to prove some useful conclusions.China is in the social transition period. An increasing number of people paid attention to social security and social stability. Through some relevant research and analysis on social phenomena and refer to some related information, this paper created a nonlinear dynamic system model on social security issues. The article analyzed the result of this model, and it was also used in some social security issues. As a result it got some useful conclusions. At last, the paper was also tested by numerical method, and demonstrates these conclusions. This is another social field's application of mathematical ecology model.The article has five parts:introduction describes the background information; the first chapter is the preliminary knowledge, explaining some math knowledge which is relevant to mathematic model; the second chapter briefly describes the mathematical models of biological populations and modeling methods; The third and forth chapter is the work done, which established nonlinear differential equations systems model about the number of security personnel and criminals. And the paper also discussed the stability of equilibrium point of the model as well as limit cycle. Finally it explained the practical significance. Chapter four is the numerical simulation of security force system model. With the help of numerical simulation and image processing, it tested and demonstrated the relevant conclusions.In addition, as a model of mathematical ecology's application in the social life, this paper aims to use simple language describes the qualitative analysis of nonlinear differential equations of the relevant conclusions. And it uses graphics to show dynamic changes in a lively way, so people can understand it, know it.