背景神经网络的多稳定性研究

项目名称： 背景神经网络的多稳定性研究

项目编号： No.61202045

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 计算机科学学科

项目作者： 徐芳

作者单位： 西南石油大学

项目金额： 21万元

中文摘要： 背景神经网络是一类与背景相关的回复式神经网络。这类神经网络很好地解释了背景对神经元活动的影响，并且深刻地揭示了大脑的工作机制。背景神经网络的多稳定性是其最重要的动力学性质之一。然而，由于原始的背景神经网络模型的复杂性，我们很难对其多稳定性进行深入的探讨。受Oja开创性工作的启发，我们将提出一系列改进的背景神经网络模型，并研究其多稳定性等相关动力学性质。我们将主要采用严格的数学理论分析与证明、计算机仿真与数值分析等研究手段，对改进的背景神经网络模型的多稳定性及相关问题进行深入研究。主要研究内容包括：改进的连续型背景神经网络模型的多稳定性分析；改进的离散型背景神经网络模型的多稳定性分析；改进的背景神经网络的分支问题研究。这些问题的研究具有较高的理论价值和应用前景。

中文关键词： 回复式神经网络；背景神经网络；多稳定性；连续吸引子；分支

英文摘要： The background neural network is a class of recurrent neural network related to background. This network provides a good interpretation of the impact of background on the activities of neurons and deeply depicts the mechanism of brain. Multistability of the background neural network is one of the most important properties of dynamics. However, because of the complexity of original background neural network model, it is very difficult to completely discuss multistability of that model. Inspired by Oja's seminal work, we shall propose a series of modified background neural network models and study on their multistability and related properties of dynamics. The main strategies we adopt are mathematically theoretical analysis and proof, computer simulation, and numerical analysis and so on. In this project, we shall mainly study on multistability of these modified background neural network models and related problems. The main contents include: the study of multistability of modified background neural networks which are continuous, the study of multistability of modified background neural networks which are discrete, and the study of their bifurcations. These studies on the above mentioned problems are higher value to both in theory and in application.

英文关键词： Recurrent neural networks；Background neural networks；Multistability；Continuous attractors；Bifurcations