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Chaotic Behaviour and Bifurcation in Real Dynamics of Two-Parameter Family of Functions including Logarithmic Map
Author
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-07-07
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
The focus of this research work is to obtain the chaotic behaviour and bifurcation in the real dynamics of a newly proposed family of functions fλ,ax=x+1−λxlnax;x>0, depending on two parameters in one dimension, where assume that λ is a continuous positive real parameter and a is a discrete positive real parameter.
This proposed family of functions is different from the existing families of functions in previous works which exhibits chaotic behaviour.
Further, the dynamical properties of this family are analyzed theoretically and numerically as well as graphically.
The real fixed points of functions fλ,ax are theoretically simulated, and the real periodic points are numerically computed.
The stability of these fixed points and periodic points is discussed.
By varying parameter values, the plots of bifurcation diagrams for the real dynamics of fλ,ax are shown.
The existence of chaos in the dynamics of fλ,ax is explored by looking period-doubling in the bifurcation diagram, and chaos is to be quantified by determining positive Lyapunov exponents.
American Psychological Association (APA)
Sajid, Mohammad. 2020. Chaotic Behaviour and Bifurcation in Real Dynamics of Two-Parameter Family of Functions including Logarithmic Map. Abstract and Applied Analysis،Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1119941
Modern Language Association (MLA)
Sajid, Mohammad. Chaotic Behaviour and Bifurcation in Real Dynamics of Two-Parameter Family of Functions including Logarithmic Map. Abstract and Applied Analysis No. 2020 (2020), pp.1-13.
https://search.emarefa.net/detail/BIM-1119941
American Medical Association (AMA)
Sajid, Mohammad. Chaotic Behaviour and Bifurcation in Real Dynamics of Two-Parameter Family of Functions including Logarithmic Map. Abstract and Applied Analysis. 2020. Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1119941
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1119941