A Class Of 2-d Discrete Nonlinear System Stability Analysis

The discussion of multi-dimensional discrete nonlinear systems appeared in 1960s.With the rapid development of spatial science and statistics,people put more attention on it.In recent research of nonlinear systems,there are abundant valuable results in one-dimensional nonlinear systems,which provide us with profound acamedic basis for the research of multidimensional discrete nonlinear systems.In this thesis,we will start with the discussion of stability of a set of 1-D discrete nonlinear systems,then a set of 2-D discrete nonlinear systems will be discussed. The content is as follows:Ⅰ. Two sets of 2-D discrete random systems.In this section,we will introduce two sets of 2-D discrete random systems which are discussed drasticly recently,and analyse the stability of the random systems. Then we present some important theories on stability and quality of the systems. Finally we will define the Lp-stability of the random systems,and then provide some sufficient and necessary conditions of the systems that can determine the stability of the random systems.Ⅱ. A set of 1-D discrete nonlinear systems.In this section, the author will mainly discuss the critical stability of a set of 1-D discrete nonlinear systems and present a value that can make the system critically stable.So that we can prepare for the two dimensional expansion in fifth chapter.Ⅲ. The analysis of the stability of a set of 2-D discrete nonlinear systems.The discussion of multi-dimensional discrete nonlinear systems appeared in 1960s,and a little amount of the development of spatial science has been created for a short time.So there are lots of difficulties in seeking relations between one-dimensional random systems and multidimensional systems. In this section,we will give a two dimensional expansion of the one-dimensional discrete nonlinear systems discussed in second chapter,and a sufficient condition of instability of the 2-D...