Journal of Engineering and Applied Sciences
ISSN: Online 1818-7803ISSN: Print 1816-949x
Abstract
In the last four decades, Chaos has been studied intensively as an interesting practical phenomenon. Hence, it is considered to be one of the most important branches in mathematics science that deals with the dynamic behavior of systems which are sensitive to the initial conditions. It has therefore been used in many scientific applications in the sciences of chemistry, physics, computers, communications, cryptography and engineering as well as in bits generators and psychology. However, there are many issues that need to be considered and highlighted such as future prediction, computational complexities and unstable behavior of dynamic system. The dynamic system must contain three characteristics in order to be considered a chaotic system which is first, to be sensitive to the initial conditions; second to have dense periodic orbits and finally to be topologically mixing. In the previous work, we studied the fixed point of a modified Jerk Map with the form MJa,b = (y-ax+by2) in order to find the contracting and expanding area of this map as well as to define the area in which the fixed points of attracting, repelling or saddle are located. In this study, we continue to address the same problem by modified Jerk Map. We prove that it has a positive Lypaunov exponent if |a| =1 and has sensitivity dependence to initial condition if |a|>1 and we give an estimate of topological entropy. Finally, to simulate our equations and obtain related results, we have used MATLAB program by implementing a Lypaunov exponent and drawing the sensitivity of MJa,b.
How to cite this article:
Samah Abdulhadi AL-Hashemi. Studying the Chaotic of Modified Jerk Map Based on Lyapunov Exponents, Topological
Entropy and Sensitivity.
DOI: https://doi.org/10.36478/jeasci.2020.3122.3127
URL: https://www.makhillpublications.co/view-article/1816-949x/jeasci.2020.3122.3127