一类分流抑制细胞神经网络的渐近概周期解

Existence of Asymptotically Almost Periodic Solution for a Class of SICNNs

带有延迟的分流抑制细胞神经网络的各种解的存在唯一性问题是微分方程方向的一个重要研究课题.为了研究一类带有混合延迟分流抑制细胞神经网络的渐近概周期解的存在性及唯一性问题,在研究过程中,依据了渐近概周期函数的唯一分解定理及其相关性质的理论,然后通过寻找适合的压缩映射并结合Banach不动点定理,研究了这类微分方程有渐近概周期解的存在性及唯一性的问题,并给出了相关的证明,所得到的结果会使这类微分方程应用更加广泛.

The existence and uniqueness problem of all kinds for shunting inhibitory cellular neural network is an important study topic of differential equation direction. In order to study the existence and uniqueness of asymp- totically almost periodic solution a class of shunting inhibitory cellular neural network with mixed delays, the condi- tions which can make this kind of equation have unique asymptotically almost periodic solution are investigated by using unique decomposition theorem of asymptotically almost periodic function and related properties, then by com- pressed mapping and combining Banach fixed point theorem, and giving the relevant proof. The results obtained will make this kind equation to be applied more widely.