Dynamics of a new generalized fractional one-dimensional map: quasiperiodic to chaotic
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Dynamics of a new generalized fractional one-dimensional map: quasiperiodic to chaotic
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Nonlinear dynamics
ISSN
0924-090X
e-ISSN
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Volume of the periodical
94
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
1377-1390
UT code for WoS article
000445930300039
EID of the result in the Scopus database
2-s2.0-85049074328