Journal of Applied Nonlinear Dynamics
Stability Analysis of Switched Complex Logistic Map in Ishikawa Orbit
Journal of Applied Nonlinear Dynamics 10(3) (2021) 381395  DOI:10.5890/JAND.2021.09.003
Shafali Agarwal
Independent Researcher, Plano, Texas 75025, USA
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Abstract
A switching strategy is also known as a Parrondo's paradox game in which the alternation of two dynamics may yield a desirable solution whereas it yielded an undesirable outcome individually. In this paper, the switching strategy is applied to the logistic map (LM) $x_{n+1}=rx_n (1x_n)$ and its variants i.e. modified LM (ModLM) and extended LM (ExLM) in Ishikawa orbit. And the alternated LM and its complex forms in terms of the control parameter value, convergence point, and chaotic range of varying changeable parameters are analyzed The experimental results show that the switching theory succeeds to achieve the required outcome, i.e. ``undesirable + undesirable = desirable'' by getting the reduced extinction range and ``chaos + chaos = order'' by converting chaotic behavior to desirable oscillatory behavior. Also, a stability range analysis of Picard, Mann, and Ishikawa iterated logistic map and its complex form is conducted to study the behavior of each map in a different orbit.
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