Learning Topological Horseshoe via Deep Neural Networks

被引：1

作者：

Yang, Xiao-Song ^{[1
,2
]}

Cheng, Junfeng ^{[1
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2024年 / 34卷 / 04期

关键词：

Poincare map; topological horseshoe; chaos; deep neural network;

D O I：

10.1142/S021812742430009X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Deep Neural Networks (DNNs) have been successfully applied to investigations of numerical dynamics of finite-dimensional nonlinear systems such as ODEs instead of finding numerical solutions to ODEs via the traditional Runge-Kutta method and its variants. To show the advantages of DNNs, in this paper, we demonstrate that the DNNs are more efficient in finding topological horseshoes in chaotic dynamical systems.

引用

页数：11

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