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An Elementary Study of Chaotic Behaviors in 1-D Maps

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Document pages: 25 pages

Abstract: In this article, we have discussed basicconcepts of one-dimensional maps like Cubic map, Sine map and analyzed their chaoticbehaviors in several senses in the unit interval. We have mainly focused on OrbitAnalysis, Time Series Analysis, Lyapunov Exponent Analysis, Sensitivity to InitialConditions, Bifurcation Diagram, Cobweb Diagram, Histogram, Mathematical Analysisby Newton’s Iteration, Trajectories and Sensitivity to Numerical Inaccuracies ofthe said maps. We have tried to make decision about these mentioned maps whetherchaotic or not on a unique interval of parameter value. We have performed numericalcalculations and graphical representations for all parameter values on that intervaland have tried to find if there is any single value of parameter for which thosemaps are chaotic. In our calculations we have found there are many values for whichthose maps are chaotic. We have showed numerical calculations and graphical representationsfor single value of the parameter only in this paper which gives a clear visualizationof chaotic dynamics. We performed all graphical activities by using Mathematicaand MATLAB.

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