@article{MAKHILLJEAS2020151619411,
    title = {Studying the Chaotic of Modified Jerk Map Based on Lyapunov Exponents, Topological
Entropy and Sensitivity},
    journal = {Journal of Engineering and Applied Sciences},
    volume = {15},
    number = {16},
    pages = {3122-3127},
    year = {2020},
    issn = {1816-949x},
    doi = {jeasci.2020.3122.3127},
    url = {https://makhillpublications.co/view-article.php?issn=1816-949x&doi=jeasci.2020.3122.3127},
    author = {Samah},
    keywords = {Chaos,modified Jerk Map,Lypaunov exponent,sensitivity dependence,entropy},
    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 MJ<sub>a,b</sub> = (y-ax+by<sup>2</sup>) 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 MJ<sub>a,b</sub>.}
    }