Mathematical consistency and long-term behaviour of a dynamical system with a self-organising vector field

DOI10.1007/s10884-020-09834-7zbMath1495.34072arXiv1812.05205OpenAlexW3008782887MaRDI QIDQ2116438

Peter E. Kloeden, Natalia B. Janson

Publication date: 17 March 2022

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.05205

zbMATH Keywords

learningplasticityself-organizationpullback attractornon-autonomous dynamical systemexplainable artificial intelligencevelocity vector field

Mathematics Subject Classification ID

Neural biology (92C20) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Asymptotic properties of solutions to ordinary differential equations (34D05) Attractors of solutions to ordinary differential equations (34D45) Nonautonomous smooth dynamical systems (37C60)

Uses Software

• DeepFace
• DeepStack

Cites Work

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• Nonautonomous and random attractors
• Asymptotic invariance and the discretisation of nonautonomous forward attracting sets
• Uniform attractors for non-autonomous random dynamical systems
• Invariant forward attractors of non-autonomous random dynamical systems
• Dynamic properties of neural networks with adapting synapses
• DeepStack: Expert-level artificial intelligence in heads-up no-limit poker
• PULLBACK ATTRACTORS OF NONAUTONOMOUS SEMIDYNAMICAL SYSTEMS
• Random Ordinary Differential Equations and Their Numerical Solution

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