Abstract
In our very recent work (2019), we extended the stability performance of logistic map up to a higher value of r using SP orbit. In this article, we further extend this range of stability by adopting switching strategy (Parrondo’s Paradox) of controlling the chaos of dynamical systems. We observe that even the earlier chaotic orbits of four step feedback procedure can be converted into periodic orbits. Our approach can be used to solve a wider circle of engineering problems.
Highlights
The dynamical systems are very sensitive on the initial conditions, i.e, it is impossible to forecast the long term behavior of the dynamical systems
Bifurcation and time series analysis have been adopting to analyze the switching strategy applied on logistic map
In the present work, the chaotic situation of logistic map has been controlled with the help of switching strategy (Parrondo’s paradox) by adopting bifurcation and time series plots
Summary
The dynamical systems are very sensitive on the initial conditions, i.e, it is impossible to forecast the long term behavior of the dynamical systems. The logistic map occupied a renowned position in understanding the complex dynamical systems due to its simplest form. It was originally introduced by P.F. Verhulst [1] to study the population of non- overlapping generation. Thereafter, a sequence of papers on Parrondo’s paradox and its applications has been published (see, [6] and references therein). Yadav et al [14], [15], controlled the chaotic behavior of superior logistic map with the help of Parrondo’s paradox. We shall apply the Parrondo’s paradox to control the chaotic behavior of logistic map considered in SP orbit [16]. Bifurcation and time series analysis have been adopting to analyze the switching strategy applied on logistic map
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