遲滯型霍普菲爾神經網路的穩定性

Abstract

類神經網路（neural networks）穩定常態解(stable stationary solution)的數目與記憶能力(memory capacity)有相對應的關係。本篇論文，我們研究遲滯型(with delay)與非遲滯型(without delay)霍普菲爾(Hopfield)神經網路之多重常態解(multiple stationary solutions)及多重週期解(multiple periodic solutions)的存在性與穩定性並估計他們相對應的吸引區域(basin of attraction)，我們藉由幾何想法設定適當的參數條件來造就這樣收斂的動態行為。最後，展示兩個數值結果的例子來驗證理論。

The number of stable stationary solutions corresponds to the memory capacity for the neural networks. In this presentation, we investigate existence and stability of multiple stationary solutions and multiple periodic solutionsfor Hopfield-type neural networks with and without delays. Their associated basins of attraction are also estimated. Such a convergent dynamical behavior is established through formulating parameter conditions based on a suitable geometrical setting. Finally, two examples are given to illustrate our main results.