Dynamics of a new generalized fractional one-dimensional map: quasiperiodic to chaotic

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18450%2F18%3A50014729" target="_blank" >RIV/62690094:18450/18:50014729 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s11071-018-4430-8" target="_blank" >http://dx.doi.org/10.1007/s11071-018-4430-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11071-018-4430-8" target="_blank" >10.1007/s11071-018-4430-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Dynamics of a new generalized fractional one-dimensional map: quasiperiodic to chaotic

Popis výsledku v původním jazyce

Discovering new chaotic maps is always essential for secure communication, cryptography, image encryption and decryption when pseudo-number generation is mandatory; however, it is still very fascinating to come across new complex dynamics of very simple maps exhibiting chaotic behavior. Despite the various forms already presented in the literature, we deal with the fractional forms of one-dimensional chaotic map with one system parameter; yet while generalization, two parameters were inserted to the map as the multiplier and the power. Therefore, in this paper, we present a novel and generalized version of a map exhibiting a strange behavior in discrete time and real number space, while detailed analyses regarding the new map with intervals of various parameters are also included. We mainly focus on a simple one-dimensional chaotic map and propose various instances with linear stability, bifurcation and Lyapunov analyses for each instance, to enhance the understanding of unstable fractional chaotic maps. It is found that the fractional map exhibits quasiperiodicity as well as periodic behavior for the smallest power parameter; while the chaotic states emerge for larger values.

Název v anglickém jazyce

Dynamics of a new generalized fractional one-dimensional map: quasiperiodic to chaotic

Popis výsledku anglicky

Discovering new chaotic maps is always essential for secure communication, cryptography, image encryption and decryption when pseudo-number generation is mandatory; however, it is still very fascinating to come across new complex dynamics of very simple maps exhibiting chaotic behavior. Despite the various forms already presented in the literature, we deal with the fractional forms of one-dimensional chaotic map with one system parameter; yet while generalization, two parameters were inserted to the map as the multiplier and the power. Therefore, in this paper, we present a novel and generalized version of a map exhibiting a strange behavior in discrete time and real number space, while detailed analyses regarding the new map with intervals of various parameters are also included. We mainly focus on a simple one-dimensional chaotic map and propose various instances with linear stability, bifurcation and Lyapunov analyses for each instance, to enhance the understanding of unstable fractional chaotic maps. It is found that the fractional map exhibits quasiperiodicity as well as periodic behavior for the smallest power parameter; while the chaotic states emerge for larger values.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Nonlinear dynamics

ISSN

0924-090X

e-ISSN

—

Svazek periodika

94

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

1377-1390

Kód UT WoS článku

000445930300039

EID výsledku v databázi Scopus

2-s2.0-85049074328