具有比例时滞和D算子的BAM神经网络概周期解的存在性与稳定性

Existence and stability of almost periodic solutions for BAM neural networks with proportional delays and operators

为了探讨一类含比例时滞和D算子的中立型BAM神经网络的概周期解的存在性与广义指数稳定性,首先,通过构造概周期函数空间,并利用压缩不动点原理,得到确保系统概周期解存在的充分条件,其次,使用微分不等式技巧得到确保系统概周期解广义指数稳定的充分条件.发现若系统的参数满足一定的条件,那么系统的概周期解是存在的,且是广义指数稳定的,而且所得结果与比例时滞无关.所得结论推进了现有文献中的相关工作.

In order to investigate the existence and generalized exponential stability of almost periodic solutions for a class of neutral type BAM neural networks with proportional delays and operators,firstly,by constructing a space of almost periodic functions and using the principle of compressed fixed points,sufficient conditions are obtained to ensure the existence of almost periodic solutions for the system.Finally,using differential inequality techniques,sufficient conditions are obtained to ensure the generalized exponential stability of almost periodic solutions for the system.It was found that if the parameters of the system satisfy certain conditions,then the almost periodic solution of the system exists and is generalized exponentially stable,and the obtained results are independent of proportional delay.The conclusions obtained have advanced the relevant work in existing literature.