连续时间神经网络的动态复杂性问题研究

项目名称： 连续时间神经网络的动态复杂性问题研究

项目编号： No.11302080

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 袁泉

作者单位： 华中科技大学

项目金额： 23万元

中文摘要： 本项目以低维连续时间Hopfield型神经网络为研究目标，研究混沌不变集随系统结构的演变规律，建立连续时间神经网络动力学系统的某些系统理论，同时也为高维神经网络的动态复杂性研究提供一定帮助和启发。研究包含：1、发现新的具有混沌性质的低维连续时间Hopfield型神经网络、细胞型神经网络（可视为具有分段线性输出函数的Hopfield型神经网络）以及Glass型基因网络（可视为具有阶梯输出函数的Hopfield型神经网络），并运用拓扑马蹄理论与计算机仿真相结合，对系统的混沌性和分岔行为给出严格的验证和证明；2、探讨连续时间神经网络的混沌性质与系统拓扑结构的联系，重点研究神经元连接的拓扑结构对系统混沌性的影响；3、研究连续时间神经网络的耦合问题，重点研究非混沌的子系统通过一定的耦合方式，得到具有混沌性质的耦合系统这一类问题，尝试从全新的角度探索混沌控制理论和神经网络产生混沌的机制。

中文关键词： 神经网络；混沌；计算机辅助证明；拓扑马蹄；

英文摘要： In order to explore the new theory of nonlinear dynamics, deepen the research of the complexity of dynamic neural network, understand parallel computing and information processing method of brain neural system, the research topics include: 1. Discover new low dimensional continuous time Hopfield neural network which have chaotic properties, cellular neural networks (as of Hopfield neural networks with piecewise linear output function) and Glass gene network (as of Hopfield neural network with multi-step output function), and prove chaotic character on these neural network models. The method of computer-assisted verification makes use of topological horseshoe theory developed by the Smale horseshoe of dynamical system combined with computer assisted. 2. Take these neural network models for instance to study the dynamical complexity of the low-dimensional continuous neural network according to topology structure of the models. We are concerned with this interesting problem in dynamics of neural networks that what connection topology will prohibit chaotic behavior in continuous time neural network and to what extent a continuous time neural network described by continuous ordinary differential equations is simple enough while can still exhibit chaos. 3. Present that chaos synchronization can take place in the coupl

英文关键词： neural network；chaos；computer assisted verification；topological horseshoe；