混沌神经网络中非稳定不动点的分布
无序系统与神经网络
2023-12-12 v3 混沌动力学
摘要
我们分析确定了一个典型混沌神经网络模型中不动点的数量与分布。该分布揭示出不动点与动力学被限制在相空间中的不同壳层上。此外，该分布使我们能够确定不动点处雅可比矩阵的特征值谱。尽管不动点与动力学在径向上相互分离，我们发现邻近的不动点充当了动力学的部分吸引性路标。
引用
@article{arxiv.2210.07877,
title = {The Distribution of Unstable Fixed Points in Chaotic Neural Networks},
author = {Jakob Stubenrauch and Christian Keup and Anno C. Kurth and Moritz Helias and Alexander van Meegen},
journal= {arXiv preprint arXiv:2210.07877},
year = {2023}
}
备注
37 pages, 11 figures. Main changes include: - additional analysis of the fixed points' role for the dynamics - replica calculation for the random determinant (removing a previous assumption) - extensive investigation of finite size effects - asymptotic results for the number of fixed points and their distribution at the edge of chaos and in the strongly chaotic limit