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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Dynamics of $q$-Deformed Logistic Map via Superior Approach

Journal of Applied Nonlinear Dynamics 12(2) (2023) 285--296 | DOI:10.5890/JAND.2023.06.007

Renu$^{1}$, Ashish$^{2}$, Renu Chugh$^{1}$

$^{1}$ Department of Mathematics, Maharshi Dayanand University, Rohtak-124001, Haryana, India

$^{2}$ Department of Mathematics, Government College Satnali, Mahendergarh-123024, Haryana, India

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Abstract

Inspired by various studies on $q$-deformations in physical systems and their wider applications in different fields, we study the $q$-deformed logistic map via a superior fixed-point feedback approach. Different dynamical characteristics such as fixed-points, time-series evolution, period-doubling bifurcation, and Lyapunov exponent of the system are analyzed using a superior approach. The results are carried out analytically as well as experimentally. Under the proposed approach, due to the presence of an additional control parameter $\alpha$, the system exhibits superior dynamical characteristics such as better stability range, suitable lower maximum Lyapunov exponent value, and an improved sensitivity as compared to the traditional approach.

Acknowledgments

This work is supported by the University Grants Commission of India under Grant No. (F.No. $16$-$6$(DEC. $2017$)/$2018$(NET/CSIR) UGC Ref. No.: 1049/(CSIR-UGC NET DEC. 2017)).

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