忆阻递归神经网络的多重稳定性理论研究

项目名称： 忆阻递归神经网络的多重稳定性理论研究

项目编号： No.61503338

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 其他

项目作者： 黄玉娇

作者单位： 浙江工业大学

项目金额： 20万元

中文摘要： 本项目研究基于忆阻器的递归神经网络的多重稳定性理论。针对无时滞忆阻递归神经网络系统和时滞忆阻递归神经网络系统，在依赖于外部输入的连接权具有切换特性的前提下，首先提出神经网络系统在连接权连续范围内及不连续点处存在多重稳定平衡点的充分条件，在神经网络维数较小的情况下，保证大量稳定平衡点的存在，降低计算负担。其次，将流形理论应用到稳定平衡点吸引域的估计中，通过不稳定平衡点的稳定流形与不稳定流形，扩大稳定平衡点的吸引域，建立具有多个神经元的忆阻神经网络系统中稳定平衡点的完全吸引域，进一步完善吸引域理论。再次，利用忆阻递归神经网络的多重稳定性理论，提出基于忆阻递归神经网络的联想记忆的设计算法，实现具有高存储容量和高识别能力的联想记忆。研究结果将改进递归神经网络的多重稳定性理论，为基于递归神经网络的联想记忆、模式识别等应用提供行之有效的理论依据和技术保证。

中文关键词： 忆阻递归神经网络；多重稳定性；吸引域；联想记忆

英文摘要： The project devotes in multiple stability theory of recurrent neural networks based on memristor. For memristive recurrent neural networks without delay and with delays, under the premise of switched connection weights dependent on external inputs, sufficient conditions for the existence of multiple stable equilibrium points will be firstly proposed for memristive recurrent neural networks in the continuous range and discontinuous points of connection weights. When dimension of neural networks is small, the conditions can ensure the existence of a larger number of stable equilibrium points. The computational burden will be reduced. Secondly, manifold theory will be applied in the estimation of domains of attraction of stable equilibrium points. By stable manifold and unstable manifolds of unstable equilibrium points, the domains of attraction of stable equilibrium points will be expanded. Complete domains of attraction of stable equilibrium points will be established for memristive recurrent neural networks with multiple neurons. The theory of domains of attraction will be improved. Thirdly, design algorithm of associative memory based on multiple stability theory of memristive recurrent neural networks will be proposed. Associative memory with high storage capacity and high ability to identify will be achieved. The research results will perfect multiple stability theory of recurrent neural networks, and provide theoretical basis and effective method for associative memory, pattern recognition and other applications.

英文关键词： Memristive recurrent neural network;Multiple stability;Domain of attraction;Associative memory