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Learning Topological Horseshoe via Deep Neural Networks

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

E-mail Address: yangxs@hust.edu.cn

Corresponding author.

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Junfeng Cheng

https://orcid.org/0009-0008-9748-3729

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

E-mail Address: ydtq19@163.com

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https://doi.org/10.1142/S021812742430009XCited by:1 (Source: Crossref)

Abstract

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.

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