<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The nature of chaos is elusive and disputed, however it can be connected to sensitivity to initial conditions caused by nonlinearity of the equations describing chaotic phenomena. A nowhere-near comprehensive list of such equations can still be shown: the Boltzmann equation, Ginzburg-Landau equation, Ishimori equation, Korteweg-de Vries equation, Landau-Lifshitz-Gilbert equation, Navier-Stokes equation, and many more. This disproportionality between input and output creates an analytically-difficult situation, one that is complicated both algebraically and numerically – however, the study of equations that are both simple and chaotic may yield useful connections between algebraic complexity and chaos. Such connections can be used to determine the simplest possible chaotic function, which can be used as a “chaotic operator” for various non-chaotic or chaotic functions, thus reducing the problem of chaos to one based strictly on algebra.</p>
</abstract>

The nature of chaos is elusive and disputed, however it can be connected to sensitivity to initial conditions caused by nonlinearity of the equations describing chaotic phenomena. A nowhere-near comprehensive list of such equations can still be shown: the Boltzmann equation, Ginzburg-Landau equation, Ishimori equation, Korteweg-de Vries equation, Landau-Lifshitz-Gilbert equation, Navier-Stokes equation, and many more. This disproportionality between input and output creates an analytically-difficult situation, one that is complicated both algebraically and numerically – however, the study of equations that are both simple and chaotic may yield useful connections between algebraic complexity and chaos. Such connections can be used to determine the simplest possible chaotic function, which can be used as a “chaotic operator” for various non-chaotic or chaotic functions, thus reducing the problem of chaos to one based strictly on algebra.

On the Study and Possible Applications of Minimally Complex Chaos

“Alexandru Ioan Cuza” University of Iaşi

“Gheorghe Asachi” Technical University of Iaşi

“Ion Ionescu de la Brad” University of Agricultural Sciences and Veterinary Medicine

Department of Exact Sciences, Faculty of Horticulture

BULETINUL INSTITUTULUI POLITEHNIC DIN IAȘI. Secția Matematica. Mecanică Teoretică. Fizică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On the Study and Possible Applications of Minimally Complex Chaos"}

The nature of chaos is elusive and disputed, however it can be connected to sensitivity to initial conditions caused by nonlinearity of the equations...

On the Study and Possible Applications of Minimally Complex Chaos

Online veröffentlicht: 17. März 2022

Seitenbereich: 21 - 29

Eingereicht: 17. Aug. 2021

Akzeptiert: 20. Sept. 2021

DOI: https://doi.org/10.2478/bipmf-2021-0013

Schlüsselwörter
turbulence, chaos, nonlinearity, attractor

© 2021 Alin Iulian Roșu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On the Study and Possible Applications of Minimally Complex Chaos

Online veröffentlicht: 17. März 2022

Seitenbereich: 21 - 29

Eingereicht: 17. Aug. 2021

Akzeptiert: 20. Sept. 2021

DOI: https://doi.org/10.2478/bipmf-2021-0013

Schlüsselwörterturbulence, chaos, nonlinearity, attractor

© 2021 Alin Iulian Roșu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Schlüsselwörter
turbulence, chaos, nonlinearity, attractor