吸引子
混乱的
相空间
动力系统理论
齐次空间
班级(哲学)
分叉
参数空间
人工神经网络
等价(形式语言)
统计物理学
数学
集合(抽象数据类型)
空格(标点符号)
等价类(音乐)
计算机科学
纯数学
拓扑(电路)
数学分析
物理
非线性系统
人工智能
组合数学
几何学
量子力学
热力学
程序设计语言
操作系统
标识
DOI:10.1080/net.13.2.195.216
摘要
The discrete-time dynamics of small neural networks is studied empirically, with emphasis laid on non-trivial bifurcation scenarios. For particular two- and three-neuron networks interesting dynamical properties like periodic, quasi-periodic and chaotic attractors are observed, many of them co-existing for one and the same set of parameters. An appropriate equivalence class of networks is defined, describing them as parametrized dynamical systems with identical dynamical capacities. Combined symmetries in phase space and parameter space are shown to generate different representatives of such a class. Moreover, conditions on the connectivity structure are suggested, which guarantee the existence of complex dynamics for a considered equivalence class of network configurations.
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