arXiv subjects

Sk Sarif Hassan

Publications and source records attributed to Sk Sarif Hassan.

2 recordsLinked to original sources

arXiv2016

Computational Complex Dynamics Of The Discrete Lorenz System

The dynamics of the classical Lorenz system is well studied in $1963$ by E. N. Lorenz. Later on, there have been an extensive studies on the classical Lorenz system with the complex variables and the discrete time Lorenz system with real variables. To the best of knowledge of the author, so far there is no study on discrete time Lorenz system in complex variables. In this article, an attempt has been made to observe and understand the discrete dynamics of the Lorenz system with complex variables. This study compares the discrete dynamics of the Lorenz system with complex variables to that of the classical Lorenz system involving real and complex variables.

math.DS↗

arXiv2016

Complex Dynamics of a Second Order Rational Difference Equation

The dynamics of the second order rational difference equation $\displaystyle{z_{n+1}=\frac{α+ z_{n-1}}{βz_n + z_{n-1}}}$ with the real parameter $α$, $β$ and arbitrary non-negative real initial conditions is investigated a decade ago. In the present manuscript, the same has been revisited considering the parameters $α$ and $β$ as complex numbers and the initial values as arbitrary complex numbers. It is found that some of the results which are valid in real line but does not valid in complex plane. The chaotic solutions of the difference equation with complex parameters are achieved, however there does not exists such solutions in the case of real parameters.

math.DS↗