Qualitative Analysis of Complex Dynamical Systems

该项目将试图 建立本地和全球 几个定性结果 人工反馈类 联想神经网络 回忆 这些结果将 以系统的方式使用， 建立合成结果。 的 P.I.会考虑连续时间 和离散时间神经网络 其可以被赋予线性或 （高阶）非线性 互连结构， 通常的S形模型或更高 阶非线性模型 神经元（例如，楼梯 非线性）。 全局定性 结果将解决 平衡点的分布 状态空间，全局稳定性， 类似物 当地定性结果 将解决 的性质和估计 平衡吸引域 收敛速度 轨迹等等 综合结果将涉及 学习和遗忘算法， 存储容量等。 私家侦探也将使用这些神经 网络成果建立 分析和设计技术 一般动力系统（包括 控制系统）， 饱和非线性 等 系统在科学中无处不在， 技术. 除了当地 全球质量 我们寻求结果， 可控性，可观测性， 稳定性等，的情况下 的控制系统。

This project will attempt to establish local and global qualitative results for several classes of artificial feedback neural networks for associative memories. These results will be used in a systematic way to establish synthesis results. The P.I. will consider continuous-time and discrete-time neural networks which may be endowed with linear or (higher order) nonlinear interconnecting structures and with the usual sigmoidal models or higher order nonlinear models for the neurons (e.g., staircase nonlinearities). Global qualitative results will address the distribution of equilibria in the state space, global stability, and the like. Local qualitative results will address the stability properties and estimates of the domain of attraction of equilibria, rates of convergence of trajectories, and so forth, Synthesis results will address learning and forgetting algorithms, storage capacity, etc. The P.I. will also use these neural networks results to establish analysis and design techniques for general dynamical systems (including control systems) endowed with saturation nonlinearities. Such systems are pervasive in science and technology. In addition to local and global qualitative characterizations, we seek results for controllability, observability, stabilizability, etc., in the case of control system.