1988年L.O.Chua and L.Yang 提出 Cellular Neural Networks , 我們用functional differential equations 來描述一維的Delayed Cellular Neural Networks ，cell上的任一點i表示 internal state，它的 dynamic除了和自己有關，也會受到feedback template 的影響 。其中feedback template 之 dynamic 是透過a 、α、β乘上它所對應的 output function 影響其 dynamic。 我們討論general 的 output function ，以及滿足 boundary conditions 的 traveling wave， 利用 properties of characteristic equation 建構 upper and lower solution，並在Banach space上定義一個 operator，利用operator的四個特性和 monotone iteration method，證明小於臨界速度時traveling wave存在滿足boundary conditions 的 non-decreasing solution 。 This paper is concerned with the existence of monotonic traveling wave solutions of cellular neural networks distributed in the one-dimensional integer lattice Z. The dynamics of each given cell depends on itself and its neighbor cells with instantaneous feedback.The profile equation of the infinite system of ordinary differential equations can be written as a functional differential equation in mixed type. By using the monotone iteration method, we show the existence of non-decreasing traveling solutions when the speed is negative enough.
