连续和离散忆阻神经网络的动力学分析与控制

项目名称： 连续和离散忆阻神经网络的动力学分析与控制

项目编号： No.61473244

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 其他

项目作者： 蒋海军

作者单位： 新疆大学

项目金额： 83万元

中文摘要： 忆阻器具有天然的记忆功能和纳米级的物理尺寸，是实现人工大脑的有力工具。本项目将忆阻器天然的信息存储功能和神经网络强大的高速并行处理能力相结合，构建并发展已有的基于忆阻器的连续神经网络模型，并利用离散化方法建立离散忆阻神经网络模型，然后采用泛函微分方程理论和 Lyapunov 泛函方法对具有不同时滞的连续和离散忆阻神经网络进行定性分析，探讨在不同意义下的Lyapunov稳定性，包括渐近稳定性，指数稳定性，绝对稳定性及鲁棒稳定性等。运用线性矩阵不等式、非光滑分析方法和分支理论，讨论基于连续和离散忆阻神经网络的耗散性、无源性和分支问题，并研究网络拓扑结构与同步行为的关系，提出行之有效的同步控制策略。最后通过仿真实验和数值模拟，验证忆阻神经网络的优势和理论研究的可行性。

中文关键词： 神经网络；忆阻器；稳定性；同步；分支

英文摘要： Memristor is a powerful tool to realize artificial brain due to it has a nanoscale physical dimensions and natural capability of memorizing. In this project, we will develop existing continuous-time memristive neural network models and establish discrete-time memristive neural network models by combining the information storage features of memristor to the high-speed parallel processing capability of neural networks. Based on the theory of functional differential equations and Lyapunov functional method, we will study Lyapunov stability of continuous-time and discrete-time memristive neural networks with time delays, such as asymptotic stability, exponential stability, absolute stability and robust stability. In addition, we will investigate the passivity, dissipativity and bifurcation of continuous-time and discrete-time memristive neural networks by employing the linear matrix inequality, nonsmooth analysis method and bifurcation theory. We will also discuss the relationships between network topology and synchronous behavior of memristive neural networks, and give some simple and novel conditions to ensure the synchronization of constructed networks. Finally, we will give some numerical examples with their numerical simulations to demonstrate the effectiveness and feasibility of the developed theoretical results.

英文关键词： Neural Network;Memristor;Stability;Synchronization;Bifurcation