IJITCS Vol. 12, No. 4, 8 Aug. 2020

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Chaotic system, Extended logistic map, Ishikawa Iteration, Modified logistic map

Recently, the logistic map is studied to analyse the impact on the chaotic dynamics of various iterated logistic maps using Picard, Mann, and many more. The purpose of this paper is to explore the behavior of a multi-scale population model, i.e. modified logistic map (Mod-LM) and chosen population proportion model, i.e. extended logistic map (Ex-LM) in an I-superior orbit using a bifurcation diagram. The additional parameters of Mod-LM and Ex-LM with the three-step iteration system, increase the degree of freedom which invariably enhances the stability of both the functions. A detailed study of possible scenarios has been conducted to discover the effect of each parameter to the fixed point and its location, periodic cycle, and stability condition by examining the corresponding bifurcation diagram. The experimental result is discussed in terms of convergence point and chaotic range of the given dynamical systems.

Shafali Agarwal, "Chaotic Dynamics of Complex Logistic Map in I-Superior Orbit", International Journal of Information Technology and Computer Science(IJITCS), Vol.12, No.4, pp.11-18, 2020. DOI:10.5815/ijitcs.2020.04.02

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