Attracting subspaces in a hyper-spherical representation of autonomous dynamical systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F17%3A00317940" target="_blank" >RIV/68407700:21230/17:00317940 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1063/1.5001891" target="_blank" >http://dx.doi.org/10.1063/1.5001891</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/1.5001891" target="_blank" >10.1063/1.5001891</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Attracting subspaces in a hyper-spherical representation of autonomous dynamical systems

Popis výsledku v původním jazyce

In this work, we focus on the possibility to recast the ordinary differential equations (ODEs) governing the evolution of deterministic autonomous dynamical systems (conservative or damped and generally non-linear) into a parameter-free universal format. We term such a representation "hyper-spherical" since the new variables are a "radial" norm having physical units of inverse-of-time and a normalized "state vector" with (possibly complex-valued) dimensionless components. Here we prove that while the system evolves in its physical space, the mirrored evolution in the hyper-spherical space is such that the state vector moves monotonically towards fixed "attracting subspaces" (one at a time). Correspondingly, the physical space can be split into "attractiveness regions." We present the general concepts and provide an example of how such a transformation of ODEs can be achieved for a class of mechanical-like systems where the physical variables are a set of configurational degrees of freedom and the associated velocities in a phase-space representation. A one-dimensional case model (motion in a bi-stable potential) is adopted to illustrate the procedure.

Název v anglickém jazyce

Attracting subspaces in a hyper-spherical representation of autonomous dynamical systems

Popis výsledku anglicky

In this work, we focus on the possibility to recast the ordinary differential equations (ODEs) governing the evolution of deterministic autonomous dynamical systems (conservative or damped and generally non-linear) into a parameter-free universal format. We term such a representation "hyper-spherical" since the new variables are a "radial" norm having physical units of inverse-of-time and a normalized "state vector" with (possibly complex-valued) dimensionless components. Here we prove that while the system evolves in its physical space, the mirrored evolution in the hyper-spherical space is such that the state vector moves monotonically towards fixed "attracting subspaces" (one at a time). Correspondingly, the physical space can be split into "attractiveness regions." We present the general concepts and provide an example of how such a transformation of ODEs can be achieved for a class of mechanical-like systems where the physical variables are a set of configurational degrees of freedom and the associated velocities in a phase-space representation. A one-dimensional case model (motion in a bi-stable potential) is adopted to illustrate the procedure.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20506 - Coating and films

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Physics

ISSN

0022-2488

e-ISSN

1089-7658

Svazek periodika

58

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

18

Strana od-do

1-18

Kód UT WoS článku

000412102600021

EID výsledku v databázi Scopus

2-s2.0-85029510529