具有环状结构的离散神经网络的混沌性  

Chaos in Discrete Neural Networks of Ring Architecture

作　　者：吴小英 陈员龙 WU Xiao-ying;CHEN Yuan-long(Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, China)

机构地区：[1]广东金融学院金融数学与统计学院

出　　处：《佳木斯大学学报（自然科学版）》2019年第3期492-495,共4页Journal of Jiamusi University：Natural Science Edition

基　　金：广东省自然科学基金(2014A030310469,2017A030313037);广东金融学院2017创新强校工程项目(20170406101)

摘　　要：研究一类具有环状结构的延迟离散神经网络的混沌性,通过使用矩阵变换方法,建立具有较好性质的无延迟时间的无穷维等价系统,通过等价系统的性质获得延迟离散神经网络在远离原点区域的一个闭不变集,并证明此神经网络系统在此闭不变集上的子系统与具有两个符号的双边符号动力系统拓扑共轭。从而证明这类具有环状结构的神经网络系统在某种条件下存在Devaney混沌。In this paper, a delayed discrete Hopfield neural networks of ring architecture is researched, by using the method of matrix transformation, the qualitative infinite dimensional equivalent systems without delay is established. Getting a closed invariant set of delay-discrete neural networks in a region by equivalent system, and proving the neural network system has topological conjugacy with the subsystem in the invariant set above. Thus it can be proved that the discrete neural networks of ring architecture has Devaney chaos under certain conditions.

关 键 词：DEVANEY混沌 离散神经网络 拓扑共轭 符号动力系统 

分 类 号：O193[理学—数学]