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A Dynamical System Model in the Social Security

Author: ZuoZengFu
Tutor: SuZhiYong
School: Lanzhou University
Course: Applied Mathematics
Keywords: Mathematical Ecology Social security Lyapunov stability Limit cycle Numerical Simulation
CLC: O175.13
Type: Master's thesis
Year: 2010
Downloads: 52
Quote: 0
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Abstract


The mathematical model is a particular object of the real world for a particular purpose , according to its internal rules , to make the necessary simplifications and assumptions , the use of a mathematical structure appropriate mathematical tools . It or be able to explain the actual state of the particular phenomena or to predict the future state of the object , or can provide a processing object optimal decisions or control. This paper uses mathematical modeling methods to study the problem of social order and social stability , and use of mathematical methods to prove some sociological theory and get some useful conclusions . China is in a period of social transition , social security and social stability by more and more people's attention . Establishment of a social security problems of nonlinear dynamical systems model through research and analysis of social phenomena , and refer to the relevant information , articles , analysis of the model solution to the social security problem , and restore some useful conclusion , the last article using numerical simulation method for testing and demonstration of these conclusions . This mathematical ecology model of an application in the social field . This paper is divided into five sections : Introduction introduces the research background of the article ; prior knowledge , mathematical modeling involved to some mathematical knowledge described ; Chapter II an overview of the mathematical models of biological populations modeling methods ; chapters III and IV of this Chapter to establish the nonlinear differential equation model of the security personnel and the number of criminals , and discuss the stability of the equilibrium point and limit cycles , and finally explains its practical significance ; Chapter of the numerical simulation of the power system model of social order , by means of numerical simulation and image processing , test and demonstrate the relevant conclusions . Application in social life as mathematical ecology model , this paper aims to use as simple language as described in the relevant conclusions of the qualitative analysis of nonlinear differential equations and graphics make these dynamic changes in the performance of the more vivid , so that people can clearly understand to know it .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Ordinary Differential Equations > Stability theory
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