Chen Jiejie, Zeng Zhigang, Jiang Ping
School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China.
Neural Netw. 2014 Dec;60:33-43. doi: 10.1016/j.neunet.2014.07.007. Epub 2014 Jul 28.
In this paper, the existence, uniqueness and stability of almost periodic solution for a class of delayed memristor-based neural networks are studied. By using a new Lyapunov function method, the neural network that has a unique almost periodic solution, which is globally exponentially stable is proved. Moreover, the obtained conclusion on the almost periodic solution is applied to prove the existence and stability of periodic solution (or equilibrium point) for delayed memristor-based neural networks with periodic coefficients (or constant coefficients). The obtained results are helpful to design the global exponential stability of almost periodic oscillatory memristor-based neural networks. Three numerical examples and simulations are also given to show the feasibility of our results.
本文研究了一类基于忆阻器的时滞神经网络概周期解的存在性、唯一性和稳定性。通过使用一种新的Lyapunov函数方法，证明了该神经网络存在唯一的全局指数稳定的概周期解。此外，将关于概周期解的所得结论应用于证明具有周期系数（或常数系数）的基于忆阻器的时滞神经网络周期解（或平衡点）的存在性和稳定性。所得结果有助于设计基于忆阻器的概周期振荡神经网络的全局指数稳定性。还给出了三个数值例子和仿真结果以表明我们结果的可行性。
