Hu Leping, Duan Lian
School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, 232001 Anhui People's Republic of China.
Cogn Neurodyn. 2024 Oct;18(5):2963-2973. doi: 10.1007/s11571-024-10129-6. Epub 2024 Jun 7.
Finite-time synchronization is a crucial phenomenon observed in nonlinear complex systems, the settling time in such a dynamic phenomenon is heavily depends on the initial states which may be unaccessible beforehand in the real world. Eliminating the dependence of the settling time on initial states leads to major advantage and convenience in practical applications. This paper is concerned with the fixed-/preassigned-time synchronization of delayed complex-valued neural networks(CVNNs) with discontinuous activations. By designing novel state feedback controllers, and with the help of Filippov regularization and inequality techniques, some new criteria for achieving fixed-/preassigned-time synchronization are established. The obtained theoretical results cover and supplement existing ones of the CVNNs with continuous activations. In addition, the upper-bound of the settling time is explicitly estimated. Finally, the validity of the theoretical results is supported by numerical simulations.
有限时间同步是在非线性复杂系统中观察到的一种关键现象，这种动态现象中的稳定时间在很大程度上取决于初始状态，而在现实世界中这些初始状态可能事先无法获取。消除稳定时间对初始状态的依赖性在实际应用中具有重要优势和便利性。本文研究具有不连续激活函数的时滞复值神经网络（CVNNs）的固定/预指定时间同步问题。通过设计新颖的状态反馈控制器，并借助菲利波夫正则化和不等式技术，建立了一些实现固定/预指定时间同步的新准则。所获得的理论结果涵盖并补充了具有连续激活函数的CVNNs的现有结果。此外，明确估计了稳定时间的上界。最后，通过数值模拟验证了理论结果的有效性。
