Stability of 1-D-CNN's with Dirichlet boundary conditions and global propagation dynamics
Stability of 1-D-CNN's with Dirichlet boundary conditions and global propagation dynamics
复制标题
具有狄利克雷边界条件和全局传播动力学的一维 CNN 的稳定性
DOI：
10.1109/81.852930
复制
发表时间：
2000
影响因子：
5.1
通讯作者：
G. Sandre
中科院分区：
文献类型：
--
作者：
G. Sandre
本文研究了一维细胞神经网络的稳定性问题。不存在周期性或混沌行为（由完全稳定性保证）是许多应用的要求。虽然已经证明了广泛类别的CNN的完全稳定性，但即使在一维CNN的子集中，仍然有一些重要的参数范围没有证据。收集结果，可以观察到，对于以全局传播动力学和相反符号模板（C=[spr]，0<p-q<|R-S|，rs<0）的Dirichlet边界条件。我们在这里给出了反对称模板（C=[sp-s]）的特殊情况下的完全稳定性的证明，也称为连通分量检测器。证明在下面指定的参数范围内有效。这里介绍的方法似乎适合扩展到更广泛的CNN类。
In this paper we face the problem of stability for monodimensional cellular neural networks (CNNs). The absence of periodic or chaotic behavior, which is guaranteed by complete stability, is a requirement for many applications. Though complete stability has been proven for wide classes of CNNs, even within the subset of monodimensional CNNs there are still some significant parameter ranges where no proof is available. Collecting results, one can observe that a stability proof is lacking for all CNNs characterized by global propagation dynamics and opposite sign template (C=[spr], 0<p-q<|r-s|, rs<0) with Dirichlet boundary conditions. We give here a proof of complete stability in the special case of antisymmetric template (C=[sp-s]), also known as the connected component detector. The proof is valid within a parameter range specified in the following. The methods here introduced appear suitable for extension to wider classes of CNN's.