Some chaotic and mixing properties of fuzzified dynamical systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F14%3AA1500R9V" target="_blank" >RIV/61988987:17610/14:A1500R9V - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Some chaotic and mixing properties of fuzzified dynamical systems

Popis výsledku v původním jazyce

Let X be a compact metric space, let phi be a continuous self-map on X, and let F(X) denote the space of fuzzy sets on X equipped with the levelwise topology. In this paper we study relations between a given (crisp) dynamical system (X, phi) and its g-fuzzification (F(X), Phi(g)). Among other things we study various (weak, strong, mild etc.) mixing properties and also several kinds of chaotic behaviors (Li-Yorke chaos, omega-chaos, distributional chaos, topological chaos etc.). We specified subspaces offuzzy sets which make sense to study further. Additionally, we proved that numerous local characteristics of the original dynamical system can be found in its fuzzy extension, while many global characteristics are preserved in the opposite direction. Thus, among other things, we obtained easy-to-check criteria for checking absence of complex behavior in induced fuzzy dynamical systems.

Název v anglickém jazyce

Some chaotic and mixing properties of fuzzified dynamical systems

Popis výsledku anglicky

Let X be a compact metric space, let phi be a continuous self-map on X, and let F(X) denote the space of fuzzy sets on X equipped with the levelwise topology. In this paper we study relations between a given (crisp) dynamical system (X, phi) and its g-fuzzification (F(X), Phi(g)). Among other things we study various (weak, strong, mild etc.) mixing properties and also several kinds of chaotic behaviors (Li-Yorke chaos, omega-chaos, distributional chaos, topological chaos etc.). We specified subspaces offuzzy sets which make sense to study further. Additionally, we proved that numerous local characteristics of the original dynamical system can be found in its fuzzy extension, while many global characteristics are preserved in the opposite direction. Thus, among other things, we obtained easy-to-check criteria for checking absence of complex behavior in induced fuzzy dynamical systems.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: Centrum excelence IT4Innovations</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

INFORM SCIENCES

ISSN

0020-0255

e-ISSN

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Svazek periodika

279

Číslo periodika v rámci svazku

20.9.2014

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

642-653

Kód UT WoS článku

000337985200044

EID výsledku v databázi Scopus

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