TITLE:
An Elementary Study of Chaotic Behaviors in 1-D Maps
AUTHORS:
Shah Abdullah Al Nahian, Zakir Hosen, Payer Ahmed
KEYWORDS:
Sensitivity, Trajectory, Numerical Inaccuracies, Orbit, Bifurcation, Cobweb Diagram
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.5,
May
29,
2019
ABSTRACT: In this article, we have discussed basic
concepts of one-dimensional maps like Cubic map, Sine map and analyzed their chaotic
behaviors in several senses in the unit interval. We have mainly focused on Orbit
Analysis, Time Series Analysis, Lyapunov Exponent Analysis, Sensitivity to Initial
Conditions, Bifurcation Diagram, Cobweb Diagram, Histogram, Mathematical Analysis
by Newton’s Iteration, Trajectories and Sensitivity to Numerical Inaccuracies of
the said maps. We have tried to make decision about these mentioned maps whether
chaotic or not on a unique interval of parameter value. We have performed numerical
calculations and graphical representations for all parameter values on that interval
and have tried to find if there is any single value of parameter for which those
maps are chaotic. In our calculations we have found there are many values for which
those maps are chaotic. We have showed numerical calculations and graphical representations
for single value of the parameter only in this paper which gives a clear visualization
of chaotic dynamics. We performed all graphical activities by using Mathematica
and MATLAB.