The aim of this paper is to investigate the control of chaotic Burke-Shaw
system using Pyragas method. This system is derived from Lorenz system which
has several applications in physics and engineering (e.g. secure
communications). The linear stability and the existence of Hopf bifurcation
of this system are investigated. Based on the characteristic equation, a
theorem is stated and proved. This theorem is used to calculate the interval
values of the time delay $ au $ at which this system is stable (unstable).
By establishing appropriate time delay $ au $ and feedback strength $K$
ranges, one of the unstable equilibria of this system can be controlled to
be stable. We, also, introduced the fractional version of this system which is not
studied in the literature as far as we know. The advantage of the fractional
order system is that, the system has extra parameter which enriches its
dynamics. Increasing the number of parameters may be used to increase the
security of the transmitted information. We apply the Pyragas method to
control the chaotic behavior of fractional Burke-Shaw system. As we did for
the integer order, we determine the values of $ au $ and $K$ which
guarantee that the fractional version is stable. Finally, to support the
analytical results, some numerical simulations are carried out which
indicate that chaotic solution is turned to be stable if $ au $ passes
through certain intervals. The bifurcation diagrams are calculated.