An Elementary Study of Chaotic Behaviors in 1-D Maps

HTML  XML Download Download as PDF (Size: 11550KB)  PP. 1149-1173  
DOI: 10.4236/jamp.2019.75077    856 Downloads   2,010 Views  

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.

Share and Cite:

Al Nahian, S. , Hosen, Z. and Ahmed, P. (2019) An Elementary Study of Chaotic Behaviors in 1-D Maps. Journal of Applied Mathematics and Physics, 7, 1149-1173. doi: 10.4236/jamp.2019.75077.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.