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Study on Reaction-diffusion Model of Educational Innovation

Author: LiShi
Tutor: ShiJiuYu
School: Harbin Engineering University
Course: Applied Mathematics
Keywords: Educational innovation Diffusion equation Differential equation model Stable condition
CLC: G40
Type: Master's thesis
Year: 2011
Downloads: 7
Quote: 0
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The previously established model aimed at teaching quality and lacked of the study about the diffusion process of educational innovation according to the analysis of the model which was established on the educational system before. Differential equation model is a very important model in the fields of population ecology and engineering technology.Based on the study about the stability theory of differential equation and the diffuse process of educational innovation reaction, this paper focus on describing the diffuse process of educational innovation reaction by using differential equation for the first time. Four representative diffusion models of educational innovation were established after considering correlations between education and environment. For seeking the optimum state between education and environment, the models were analyzed according to the stability theory of differential. These models supplied theory testify for imitating and predicting the replacement of new and old education、the evolution process of results and constructing research-based university.This paper contains five chapters. In chapterⅠ, the basic conception purpose and significance of the educational innovation diffusion were introduced. The study trend of the model of differential equation at home and abroad was analyzed and the research method was introduced briefly. Finally, the research content of this paper was summarized.In chapterⅡ, theory of stability of the differential equation as the pre-knowledge about this research was introduced in details. Theory of stability of the differential equation was divided one-order differential equations of stationary point and stability and the second order differential equations of stationary point and stability, respectively. The subject research analysis about the second order differential equations of stationary point and stability is especially important in this research. The analytical method about establishing model will be used in chapterⅢandⅣ.In chapterⅢ, four models established on aiming at educational innovation diffusion were introduced in details. First, a model was established to analyze the condition of containing an effect of educational innovation diffusion. Then the condition of two kinds of educational innovation worked simultaneously in the same educational system was analyzed. According to the correlations between both diffuse sides, educational model、educational competition model and educational substitute model were established. Three models were analyzed by using pre-knowledge of characterⅡ.CharacterⅣexpanded the applications of the model of differential equation into other fields including population ecology, technological innovation, production innovation and human-earth relations, and established the model of differential equation, respectively. Especially in human-earth relations, the external factor of emission reduction was considered and the model of human-earth was explained through differential equation stable theory.In characterⅤ, three relations of both diffuse sides were obtained when two kinds of innovation diffuse were existed in a system by classifying and analyzing models mentioned in this paper. The conclusion, innovation and disadvantage of this research were obtained by analyzing the interrelations among three models and in different fields and the analysis of models in details.

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