School of Mathematics and Statistics, Anhui Normal University, Wuhu, Anhui 241000, China; MOE-LCSM, School of Mathematical Sciences and Statistics, Hunan Normal University, Changsha 410081, China.
MOE-LCSM, School of Mathematical Sciences and Statistics, Hunan Normal University, Changsha 410081, China.
Neural Netw. 2023 Sep;166:354-365. doi: 10.1016/j.neunet.2023.07.017. Epub 2023 Jul 17.
This paper aims to study the fixed-time stabilization of a class of delayed discontinuous reaction-diffusion Cohen-Grossberg neural networks. Firstly, by providing some relaxed conditions containing indefinite functions and based on inequality techniques, a new fixed-time stability lemma is given, which can improve the traditional ones. Secondly, based on state-dependent switching laws, the periodic wave solution of the formulated networks is transformed into the periodic solution of ordinary differential system. By utilizing differential inclusions theory and coincidence theorem, the existence of periodic solutions is obtained. Thirdly, based on the new fixed-time stability lemma, the periodic solutions are stabilized at zero in a fixed-time, which is a new topic on reaction-diffusion networks. Moreover, the established criteria are all delay-dependent, which are less conservative than the previous delay-independent ones for ensuring the stabilization of delayed reaction-diffusion networks. Finally, two examples give numerical explanations of the proposed results and highlight the influence of delays.
本文旨在研究一类时滞不连续反应扩散 Cohen-Grossberg 神经网络的固定时间稳定性。首先，通过提供一些包含不定函数的更宽松条件，并基于不等式技术，给出了一个新的固定时间稳定性引理，该引理可以改进传统引理。其次，基于状态相关切换律，将所提出的网络的周期波解转化为常微分系统的周期解。利用微分包含理论和重合度定理，得到了周期解的存在性。第三，基于新的固定时间稳定性引理，在固定时间内将周期解稳定在零，这是反应扩散网络的一个新课题。此外，所建立的准则均为时滞相关，与保证时滞反应扩散网络稳定性的先前时滞无关准则相比，它们的保守性更小。最后，两个例子给出了所提出结果的数值解释，并强调了时滞的影响。
