教育创新的反应扩散模型的研究

发布时间：2018-04-08 18:07

本文选题：教育创新　切入点：扩散方程　出处：《哈尔滨工程大学》2011年硕士论文

【摘要】：分析以往针对教育系统建立的模型发现,以前所建立起来的模型,往往只是针对教学质量,在对教育创新扩散过程进行的研究方面还很欠缺。而微分方程模型在种群生态学和工程技术领域中都是一类十分重要的模型,但在研究教育创新上还未曾应用。本文在充分研究微分方程稳定性理论和教育创新反应扩散过程的基础上,将两者相融合,首次提出用微分方程来描述教育创新反应扩散过程。在充分考虑教育与环境之间的相互关系的基础上,建立了四个具有代表性的教育创新反应扩散模型。再根据微分方程定性理论,对所建立的模型进行了分析,以寻求教育与环境之间的最佳协调状态。这些模型为模拟与预测新旧教育更替、结果演变过程及构建研究型大学提供理论依据。本课题研究分为五个部分进行,在第1章绪论中,介绍了教育创新扩散的基本概念、研究的目的和意义,分析了国内、外本课题微分方程模型的研究动态,并简要介绍了本课题的研究方法,对本篇论文的研究内容做了一次总体概括。第2章详细介绍了本次课题研究所要运用到的预备知识：微分方程稳定性理论。微分方程稳定性理论又分为一阶微分方程的平衡点及稳定性,以及二阶微分方程的平衡点及稳定性。其中对二阶微分方程平衡点及稳定性的分析对本课题研究尤为重要,在第3章和第4章对所建立模型进行分析时,将用到此方法。在本文的第3章,详细介绍针对教育创新反应扩散所建立的四个模型。首先对只有一种创新教育扩散效应的情况进行建模分析,然后分析在同一教育系统中有两种创新教育同时发生扩散的情况,根据扩散双方可能存在的相互关系,建立了教育竞争型、教育互补型和教育替代型,并对此三种模型运用第2章中介绍的预备知识进行模型分析。在本文第4章,对微分方程模型在其他领域的应用做了扩展。所扩展到的领域包括种群生态学、技术创新领域、产品创新领域、人地关系的研究领域,并分别对其建立了微分方程模型。特别是,在对人地关系的研究领域建模时,考虑到了“减排”的外在因素,最后用微分方程稳定性理论,对在“减排”下的人地关系模型进行了重点说明。第5章,将本课题研究所涉及到的模型进行归类分析,得到了在同一系统中存在两种创新扩散时扩散同时发生时的三种关系,分析这三类关系在不同领域的相互联系,这三种模型间的相互联系,以及对文中所建立模型的具体分析,得到了本课题研究的结论、创新点及不足。
[Abstract]:By analyzing the previous models of education system, it is found that the models established before are often only aimed at the quality of teaching and lack of research on the diffusion process of educational innovation.The differential equation model is a kind of very important model in the field of population ecology and engineering technology, but it has not been applied in the research of educational innovation.On the basis of fully studying the stability theory of differential equations and the process of educational innovation reaction diffusion, this paper proposes to describe the process of educational innovation reaction diffusion by differential equation for the first time.On the basis of fully considering the relationship between education and environment, four representative models of educational innovation reaction diffusion are established.Based on the qualitative theory of differential equation, the model is analyzed to find the best coordination between education and environment.These models provide theoretical basis for simulating and predicting the change of old and new education, the evolution process of results and the construction of research universities.This research is divided into five parts. In the first chapter, the author introduces the basic concept of educational innovation diffusion, the purpose and significance of the research, and analyzes the domestic and foreign research trends of the differential equation model.The research methods of this paper are briefly introduced, and the research content of this paper is summarized in a general way.In chapter 2, we introduce the theory of stability of differential equation.The stability theory of differential equation is divided into the equilibrium point and stability of the first order differential equation and the equilibrium point and stability of the second order differential equation.The analysis of the equilibrium point and stability of second order differential equation is particularly important to the research of this subject. This method will be used in the analysis of the established model in chapters 3 and 4.In chapter 3, four models of educational innovation reaction diffusion are introduced in detail.First, we model and analyze the diffusion effect of only one kind of innovation education, and then we analyze that there are two kinds of innovation education in the same educational system, and that there are two kinds of innovation education diffusion at the same time, according to the possible relationship between diffusion and diffusion.The educational competition type, the educational complementary type and the educational substitution type are established, and the three models are analyzed by using the preparatory knowledge introduced in Chapter 2.In chapter 4, the application of differential equation model in other fields is extended.The extended fields include population ecology, technological innovation, product innovation, and the research field of man-earth relationship. The differential equation models are established respectively.In particular, when modeling the human-land relationship, the external factors of "emission reduction" are taken into account. Finally, the man-land relationship model under "emission reduction" is explained emphatically by using the stability theory of differential equation.The relationship between the three models and the concrete analysis of the models established in this paper, the conclusions, innovations and shortcomings of the research are obtained.
【学位授予单位】：哈尔滨工程大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：G40;O175

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