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Complexities of differentiable dynamical systems [PDF]

Journal of Mathematical Physics, 2020
We define the notion of localizable property for a dynamical system. Then, we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems. These notions are the fast growth of the number of periodic points, the positive entropy, and the high emergence.
Pierre Berger
semanticscholar   +8 more sources

Classical Fisher information for differentiable dynamical systems [PDF]

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023
Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a form of uncertainty.
Mohamed Sahbani, Swetamber Das, Jason R. Green   +2 more
semanticscholar   +7 more sources

DIFFERENTIABLE DYNAMICAL SYSTEMS [PDF]

Bulletin of the American Mathematical Society, 1967
This is a survey article on the area of global analysis defined by differentiable dynamical systems or equivalently the action (differentiable) of a Lie group G on a manifold M. An action is a homomorphism G→Diff(M) such that the induced map G×M→M is differentiable.
S. Smale
openaire   +4 more sources

Noise-aware training of neuromorphic dynamic device networks [PDF]

Nature Communications
In materio computing offers the potential for widespread embodied intelligence by leveraging the intrinsic dynamics of complex systems for efficient sensing, processing, and interaction.
Luca Manneschi, Ian T. Vidamour, Kilian D. Stenning, Charles Swindells, Guru Venkat, David Griffin, Lai Gui, Daanish Sonawala, Denis Donskikh, Dana Hariga, Elisa Donati, Susan Stepney, Will R. Branford, Jack C. Gartside, Thomas J. Hayward, Matthew O. A. Ellis, Eleni Vasilaki   +16 more
doaj   +2 more sources

Geometric Neural Ordinary Differential Equations: From Manifolds to Lie Groups [PDF]

Entropy
Neural ordinary differential equations (neural ODEs) are a well-established tool for optimizing the parameters of dynamical systems, with applications in image classification, optimal control, and physics learning.
Yannik P. Wotte, Federico Califano, Stefano Stramigioli   +2 more
doaj   +2 more sources

Homomorphisms of differentiable dynamical systems [PDF]

Kyoto Journal of Mathematics, 1974
Toshio Niwa
openalex   +3 more sources

Sampled-Data Consensus for Networked Euler-Lagrange Systems With Differentiable Scaling Functions

IEEE Access, 2021
This paper is concerned with the sampled-data consensus of networked Euler-Lagrange systems. The Euler-Lagrange system has enormous advantages in analyzing and designing dynamical systems.
Yilin Wang, Shuanghe Yu, Xinjian Xiang, Youbing Zhang   +3 more
doaj   +1 more source

Differentiability of the Largest Lyapunov Exponent for Non-Planar Open Billiards

Mathematics, 2023
This paper investigates the behaviour of open billiard systems in high-dimensional spaces. Specifically, we estimate the largest Lyapunov exponent, which quantifies the rate of divergence between nearby trajectories in a dynamical system.
Amal Al Dowais
doaj   +1 more source

A Mean-Field Game Control for Large-Scale Swarm Formation Flight in Dense Environments

Sensors, 2022
As an important part of cyberphysical systems (CPSs), multiple aerial drone systems are widely used in various scenarios, and research scenarios are becoming increasingly complex.
Guofang Wang, Wang Yao, Xiao Zhang, Ziming Li   +3 more
doaj   +1 more source

Numerical Modeling Tools and S-derivatives

Моделирование и анализ информационных систем, 2022
Numerical study of various processes leads to the need of clarification (extensions) of the limits of applicability of computational constructs and modeling tools.
Anatoly Nikolaevich Morozov
doaj   +1 more source