Coupled Discrete Fractional-Order Logistic Maps

Coupled Discrete Fractional-Order Logistic Maps

This paper studies a system of coupled discrete fractional-order logistic maps, modeled by Caputo’s delta fractional difference, regarding its numerical integration and chaotic dynamics. Some interesting new dynamical properties and unusual phenomena from this coupled chaotic-map system are revealed...

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Main Authors: Marius-F. Danca, Michal Fečkan, Nikolay Kuznetsov, Guanrong Chen
Format: Article
Language:English
Published: MDPI AG 2021-09-01
Series:Mathematics
Subjects:
discrete fractional-order system
caputo delta fractional difference
fractional-order difference equation
stability
hidden attractor
Online Access:https://www.mdpi.com/2227-7390/9/18/2204
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spelling doaj-655d693121a14e2b90b71c9e42d4d8862021-09-26T00:37:56ZengMDPI AGMathematics2227-73902021-09-0192204220410.3390/math9182204Coupled Discrete Fractional-Order Logistic MapsMarius-F. Danca0Michal Fečkan1Nikolay Kuznetsov2Guanrong Chen3Romanian Institute of Science and Technology, 400504 Cluj-Napoca, RomaniaFaculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, 84215 Bratislava, SlovakiaMathematics and Mechanics Faculty, Saint-Petersburg State University, 199034 Saint Petersburg, RussiaDepartment of Electronic Engineering, City University of Hong Kong, Hong Kong, ChinaThis paper studies a system of coupled discrete fractional-order logistic maps, modeled by Caputo’s delta fractional difference, regarding its numerical integration and chaotic dynamics. Some interesting new dynamical properties and unusual phenomena from this coupled chaotic-map system are revealed. Moreover, the coexistence of attractors, a necessary ingredient of the existence of hidden attractors, is proved and analyzed.https://www.mdpi.com/2227-7390/9/18/2204discrete fractional-order systemcaputo delta fractional differencefractional-order difference equationstabilityhidden attractor
collection DOAJ
language English
format Article
sources DOAJ
author Marius-F. Danca
Michal Fečkan
Nikolay Kuznetsov
Guanrong Chen
spellingShingle Marius-F. Danca
Michal Fečkan
Nikolay Kuznetsov
Guanrong Chen
Coupled Discrete Fractional-Order Logistic Maps
Mathematics
discrete fractional-order system
caputo delta fractional difference
fractional-order difference equation
stability
hidden attractor
author_facet Marius-F. Danca
Michal Fečkan
Nikolay Kuznetsov
Guanrong Chen
author_sort Marius-F. Danca
title Coupled Discrete Fractional-Order Logistic Maps
title_short Coupled Discrete Fractional-Order Logistic Maps
title_full Coupled Discrete Fractional-Order Logistic Maps
title_fullStr Coupled Discrete Fractional-Order Logistic Maps
title_full_unstemmed Coupled Discrete Fractional-Order Logistic Maps
title_sort coupled discrete fractional-order logistic maps
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-09-01
description This paper studies a system of coupled discrete fractional-order logistic maps, modeled by Caputo’s delta fractional difference, regarding its numerical integration and chaotic dynamics. Some interesting new dynamical properties and unusual phenomena from this coupled chaotic-map system are revealed. Moreover, the coexistence of attractors, a necessary ingredient of the existence of hidden attractors, is proved and analyzed.
topic discrete fractional-order system
caputo delta fractional difference
fractional-order difference equation
stability
hidden attractor
url https://www.mdpi.com/2227-7390/9/18/2204
work_keys_str_mv AT mariusfdanca coupleddiscretefractionalorderlogisticmaps
AT michalfeckan coupleddiscretefractionalorderlogisticmaps
AT nikolaykuznetsov coupleddiscretefractionalorderlogisticmaps
AT guanrongchen coupleddiscretefractionalorderlogisticmaps
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