Affiliation:
1. Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan
2. Department of Mathematical Science, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia
Abstract
The local dynamics, chaos, and bifurcations of a discrete Brusselator system are investigated. It is shown that a discrete Brusselator system has an interior fixed point
if
. Then, by linear stability theory, local dynamical characteristics are explored at interior fixed point
. Furthermore, for the discrete Brusselator system, the existence of periodic points is investigated. The existence of bifurcations around an interior fixed point is also investigated and proved that the discrete Brusselator model undergoes hopf and flip bifurcations if
and
, respectively. The next feedback control method is utilized to stabilize the chaos that exists in the discrete Brusselator system. Finally, obtained results are verified numerically.
Subject
Multidisciplinary,General Computer Science