几类模糊差分方程解的性态研究
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摘要
本篇博士学位论文由四章组成.
第一章,简述有关模糊微分方程,模糊差分方程的研究发展状况,问题产生的背景和本文的主要工作及一些预备知识。
第二章,我们用模糊集的α-截集和一些分析技巧分别讨论了一阶线性模糊差分方程xn+1=Axn+B和一阶非线性模糊差分方程xn+1=(?),得到两类模型正解的存在唯一性、有界性、持久性和正平衡点的稳定性充分条件。所得结果具有一般性并改进了已有的相关结论。
第三章,我们用模糊集的α-截集和常差分方程理论讨论如下三类二阶非线性模糊差分方程模型
分别得到方程正解的存在性、有界性、持久性及平衡点全局渐近稳定和正解振动的充分条件,所得结果改进了已有文献的相关结论。
第四章,我们用模糊集的α-截集和常差分方程理论讨论如下两类高阶非线性模糊差分方程
分别得到方程正解的存在性、有界性、持久性和平衡点的稳定性的一些充分条件。
This Ph.D.thesis is divided into four chapters and main contents are as follows:
In Chapter 1, we give a survey to the developments of fuzzy differential equa-tions and fuzzy difference equations. Then we introduce the background of prob-lems, the main results of this dissertation and some preliminaries are also sum-marized.
In Chapter 2, we study respectively the first order linear fuzzy difference equation xn+1= Axn+B and the first order Riccati fuzzy difference equation xn+i =(?). By means ofα-cuts of fuzzy sets and some analysis techniques, the results about the existence, uniqueness, boundedness and persistence of the positive solution to these two models are obtained. A set of sufficient conditions are obtained for the stability of positive equilibrium point of these two models. Our conclusions are general and extend some existing ones.
In Chapter 3, Three classes second order nonlinear fuzzy difference equations, that is are studied. By using ofα-cuts of fuzzy sets and the theory of the system of ordinary difference equations, the results about the existence, uniqueness, bound-edness and persistence of the positive solution to these models are obtained. Some sufficient conditions are established for the stability of positive equilibrium point and the oscillation of positive solution, respectively. Also, our results improve the known ones.
In Chapter 4, we consider two kinds high order nonlinear fuzzy difference equations in the following
By means ofα-cuts of fuzzy sets and the theory of the system of ordinary dif-ference equations, the results about the existence, uniqueness, boundedness and persistence of the positive solution to the two models are obtained. Some suf-ficient conditions are established for the stability of positive equilibrium point, respectively.
第一章,简述有关模糊微分方程,模糊差分方程的研究发展状况,问题产生的背景和本文的主要工作及一些预备知识。
第二章,我们用模糊集的α-截集和一些分析技巧分别讨论了一阶线性模糊差分方程xn+1=Axn+B和一阶非线性模糊差分方程xn+1=(?),得到两类模型正解的存在唯一性、有界性、持久性和正平衡点的稳定性充分条件。所得结果具有一般性并改进了已有的相关结论。
第三章,我们用模糊集的α-截集和常差分方程理论讨论如下三类二阶非线性模糊差分方程模型
分别得到方程正解的存在性、有界性、持久性及平衡点全局渐近稳定和正解振动的充分条件,所得结果改进了已有文献的相关结论。
第四章,我们用模糊集的α-截集和常差分方程理论讨论如下两类高阶非线性模糊差分方程
分别得到方程正解的存在性、有界性、持久性和平衡点的稳定性的一些充分条件。
This Ph.D.thesis is divided into four chapters and main contents are as follows:
In Chapter 1, we give a survey to the developments of fuzzy differential equa-tions and fuzzy difference equations. Then we introduce the background of prob-lems, the main results of this dissertation and some preliminaries are also sum-marized.
In Chapter 2, we study respectively the first order linear fuzzy difference equation xn+1= Axn+B and the first order Riccati fuzzy difference equation xn+i =(?). By means ofα-cuts of fuzzy sets and some analysis techniques, the results about the existence, uniqueness, boundedness and persistence of the positive solution to these two models are obtained. A set of sufficient conditions are obtained for the stability of positive equilibrium point of these two models. Our conclusions are general and extend some existing ones.
In Chapter 3, Three classes second order nonlinear fuzzy difference equations, that is are studied. By using ofα-cuts of fuzzy sets and the theory of the system of ordinary difference equations, the results about the existence, uniqueness, bound-edness and persistence of the positive solution to these models are obtained. Some sufficient conditions are established for the stability of positive equilibrium point and the oscillation of positive solution, respectively. Also, our results improve the known ones.
In Chapter 4, we consider two kinds high order nonlinear fuzzy difference equations in the following
By means ofα-cuts of fuzzy sets and the theory of the system of ordinary dif-ference equations, the results about the existence, uniqueness, boundedness and persistence of the positive solution to the two models are obtained. Some suf-ficient conditions are established for the stability of positive equilibrium point, respectively.
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