Department of Mathematics, Chongqing Normal University, Chongqing, 401331 China.
Department of Mathematics, Southeast University, Nanjing, 210096 China ; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia.
Cogn Neurodyn. 2015 Apr;9(2):113-28. doi: 10.1007/s11571-014-9307-z. Epub 2014 Aug 26.
This paper investigates drive-response synchronization for a class of neural networks with time-varying discrete and distributed delays (mixed delays) as well as discontinuous activations. Strict mathematical proof shows the global existence of Filippov solutions to neural networks with discontinuous activation functions and the mixed delays. State feedback controller and impulsive controller are designed respectively to guarantee global exponential synchronization of the neural networks. By using Lyapunov function and new analysis techniques, several new synchronization criteria are obtained. Moreover, lower bound on the convergence rate is explicitly estimated when state feedback controller is utilized. Results of this paper are new and some existing ones are extended and improved. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.
本文研究了一类具有时变离散和分布时滞（混合时滞）以及不连续激活函数的神经网络的驱动-响应同步问题。严格的数学证明表明，具有不连续激活函数和混合时滞的神经网络存在 Filippov 解的全局存在性。分别设计了状态反馈控制器和脉冲控制器，以保证神经网络的全局指数同步。通过使用 Lyapunov 函数和新的分析技术，得到了几个新的同步判据。此外，当使用状态反馈控制器时，还显式估计了收敛速率的下界。本文的结果是新的，扩展和改进了一些现有的结果。最后，给出了数值模拟结果以验证理论结果的有效性。
