This paper investigates the exponential stability of traveling wave solutions for nonlinear delayed cellular neural networks. As a continuity of the past work (Wu and Niu, 2016; Yu, et al., 2011) on the existence and uniqueness of the traveling wave solutions, it is very reasonable and interesting to consider the exponential stability of the traveling wave solutions. By the weighted energy method, comparison principle and the first integral mean value theorem, this paper proves that, for all monotone traveling waves with the wave speed \(c < c_1^ \ast < 0\) or \(c > c_2^ \ast > 0\), the solutions converge time-exponentially to the corresponding traveling waves, when the initial perturbations decay at some fields.

本文研究非线性延迟细胞神经网络行波解的指数稳定性。作为过去关于行波解的存在性和唯一性的工作（Wu and Niu, 2016; Yu, et al., 2011）的延续，考虑行波解的指数稳定性是非常合理和有趣的。本文通过加权能量法、比较原理和第一积分均值定理证明，对于所有波速为\(c < c_1^ \ast < 0\)或\(c > c_2^ \ ast > 0\)，当初始扰动在某些场衰减时，解以时间指数方式收敛到相应的行波。