2020 Chaotic Behaviour and Bifurcation in Real Dynamics of Two-Parameter Family of Functions including Logarithmic Map
Mohammad Sajid
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Abstr. Appl. Anal. 2020: 1-13 (2020). DOI: 10.1155/2020/7917184


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,a(x)=x+(1λx) ln ax;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,a(x) 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,a(x) are shown. The existence of chaos in the dynamics of fλ,a(x) is explored by looking period-doubling in the bifurcation diagram, and chaos is to be quantified by determining positive Lyapunov exponents.


The author gratefully acknowledges Deanship of Scientific Research, Qassim University, Saudi Arabia, for providing financial support to conduct this research under the project grant number 3666-qec-2018-1-14-S for the year 2018-2019 AD/1440-1441 AH.


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Mohammad Sajid. "Chaotic Behaviour and Bifurcation in Real Dynamics of Two-Parameter Family of Functions including Logarithmic Map." Abstr. Appl. Anal. 2020 1 - 13, 2020. https://doi.org/10.1155/2020/7917184


Received: 2 January 2020; Revised: 24 May 2020; Accepted: 9 June 2020; Published: 2020
First available in Project Euclid: 28 July 2020

Digital Object Identifier: 10.1155/2020/7917184

Rights: Copyright © 2020 Hindawi


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