Dynamical behavior of \(q\)-deformed logistic map in superior orbit

Renu Badsiwal, Sudesh Kumari, Renu Chugh

Abstract


In this paper, we study the \(q\)-deformed logistic map in Mann orbit (superior orbit) which is a two-step fixed point iterative algorithm. The main aim of this paper is to investigate the whole dynamical behavior of the map through various techniques such as fixed point and stability approach, time-series analysis, bifurcation plot, Lyapunov exponent and cobweb diagram. We notice that the chaotic behavior of \(q\)-deformed map can be controlled by choosing control parameters carefully. Also, the convergence and stability range of the map can be increased substantially. This map may have better applications than that of standard logistic map in various situations.


Keywords


Logistic map, q-deformation, Mann orbit, time series analysis, bifurcation plot, Lyapunov exponent (LE), cobweb plot.

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2024.1.10

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