Phase and anti-phase synchronizations of fractional order hyperchaotic systems with uncertainties and external disturbances using nonlinear active control method

Abstract

In this paper, the phase and anti-phase synchronizations between fractional order hyperchaotic Lu and 4D integral order systems with parametric uncertainties and disturbances are studied using nonlinear active control method. A new lemma is used to design the controller. Numerical simulations are presented to demonstrate the effectiveness of the method to synchronize and anti-synchronize the fractional order hyperchaotic systems. The striking feature of the article is the comparison of time of synchronization and anti-synchronization with and without the presence of uncertainties and external disturbances through graphical presentations for different particular cases. © 2015, Springer-Verlag Berlin Heidelberg.