Artificial Neural Network as a Universal Model of Nonlinear Dynamical Systems

DOI10.20537/nd210102OpenAlexW3155030367MaRDI QIDQ4999680

Anna V. Kuptsova, Pavel V. Kuptsov, Nataliya V. Stankevich

Publication date: 2 July 2021

Published in: Nelineinaya Dinamika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.05402

zbMATH Keywords

neural networkLyapunov exponentsdynamical systemnumerical solutionuniversal approximation theorem

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Simulation of dynamical systems (37M05) Numerical chaos (65P20)

Uses Software

• CUDA
• Python
• TensorFlow
• PyTorch
• Adam

Cites Work

• Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. I: Theory
• Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle
• Multilayer feedforward networks are universal approximators
• The Lorenz equations: bifurcations, chaos, and strange attractors
• An equation for continuous chaos
• A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems
• Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations
• Deterministic Nonperiodic Flow
• Applied probability before 1964, and after 2014
• Approximation by superpositions of a sigmoidal function
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