论文标题
混乱的离散时间连续状态HOPFIELD网络，具有分段式激活功能
A chaotic discrete-time continuous-state Hopfield network with piecewise-affine activation functions
论文作者
论文摘要
我们构建了一个混乱的离散时间连续状态HOPFIELD网络，具有分段效果的非负激活功能和带有小正面条目的权重矩阵。更确切地说，存在一个在状态空间中的cantor集合$ c $，因此网络对$ c $的初始状态的初始状态具有敏感的依赖，并且每个初始状态的网络轨道$ c $中的$ c $具有$ c $，作为其$ω$ limit set。我们使用的方法是基于最近开发和使用的工具，用于研究分段汇总的拓扑动态。明确给出了混沌网络的参数。
We construct a chaotic discrete-time continuous-state Hopfield network with piecewise-affine nonnegative activation functions and weight matrix with small positive entries. More precisely, there exists a Cantor set $C$ in the state space such that the network has sensitive dependence on initial conditions at initial states in $C$ and the network orbit of each initial state in $C$ has $C$ as its $ω$-limit set. The approach we use is based on tools developed and employed recently in the study of the topological dynamics of piecewise-contractions. The parameters of the chaotic network are explicitly given.
