Global dynamic behaviour of a three-cell connected component detector cnn
Global dynamic behaviour of a three-cell connected component detector cnn
复制标题
三细胞连通分量检测器 cnn 的全局动态行为
DOI：
10.1002/cta.4490230204
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
M. Gilli
中科院分区：
文献类型：
--
作者：
P. Civalleri;M. Gilli
解决了模板 [-s, p, s] 描述的三单元连通分量检测器 CNN 的全局动态行为。在 p-1 > s > O 的情况下，稳定平衡的吸引力域和鞍点的稳定流形的结构通过合适的平面图表示。在 s > p - 1 > O 的情况下，显示出现五个稳定极限环和两个不稳定极限环。证明了其中一个稳定循环完全位于平面 x1 = -x3 上，而其他稳定循环具有第二个单元仅工作在输出特性的线性部分的特性。此外，发现稳定循环的吸引域被不稳定平衡的稳定流形（对于 s > p - 1 > O 仍然存在）和上述两个不稳定极限循环的稳定流形分开。
The global dynamic behaviour of a three-cell connected component detector CNN described by the template [-s, p, s] is addressed. In the case p-1 > s > O the structure of the domains of attraction of the stable equilibria and the stable manifolds of the saddle points is represented by means of a suitable planar graph. In the case s > p - 1 > O it is shown that five stable and two unstable limit cycles occur. It is proved that one of the stable cycles lies entirely on the plane x1 = -x3 whereas the others have the property that the second cell works only in the linear part of the output characteristic. Moreover, the domains of attraction of the stable cycles are found to be separated by the stable manifolds of the unstable equilibria (still existing for s > p - 1 > O ) and of the above two unstable limit cycles.