1X2 細胞型神經網路之動機分類

Abstract

這篇論文主要是研究1×2細胞型神經網路(CNN)。我們知道當CNN是dissipative 時，它會形成一個global attractor；另外，在之前的文獻已證明了:若CNN的template是對稱、且細胞數是有限個的，則CNN是completely stable。在這情形之下，我們知道global attractor包含了平衡點及其平衡點的unstable manifolds，而平衡點之間的連接軌跡會存在這些unstable manifolds。 對於template是對稱的1×2 CNN來說，分類平衡點之間的連接軌跡就決定了其動態。於是，在我們限定的regular parameters之下，所有平衡點之間的連接關係都可被分類；我們利用向量場的分析得到了這些相連軌跡的形狀及位置。這個學習希望能激起未來在CNN態方面的研究。

This presentation investigates the dynamics of a 1X2 cellular neural network. As CNN is dissipative, it possesses a global attractor. In addition, it has been shown in a previous literature that CNN with symmetric template and with finitely many cells is completely stable. Under this circumstance, the global attractor contains only equilibria and the unstable manifolds of the equilibria. The connecting orbits between equilibria lie on these unstable manifolds. Therefore, for 1X2 cellular neural network with symmetric template, the dynamics are determined through characterizing the connecting orbits between equilibria. In this investigation, all the connecting orbits between equilibria can be classified, for regular parameters. Vector field analysis as well as numerical experiments are also performed to obtain the configurations and the locations of these connecting orbits. This study hopes to stir up further inspiration in the studies of dynamics for CNN.