This paper discusses the continuous effect of the fractional order parameter of the Lü system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters. © 2014 .
Radwan A.G., Moaddy K., Salama K.N., Momani S., Hashim I.
Chaotic systems; Control; Fractional calculus; Fractional order synchronization; Non-standard finite difference schemes; Switching control
Journal of Advanced Research, Vol. 5, PP. 125 to 132, Doi: 10.1016/j.jare.2013.01.003