Chaos control of integer and fractional orders of chaotic Burke-Shaw system using time delayed feedback control

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 τ 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 τ passes through certain intervals. The bifurcation diagrams are calculated.