Reduced-order synchronization of chaotic systems with parameters unknown

In this Letter, we investigate the reduced-order synchronization of uncertain chaotic systems. Based upon the parameters modulation and the adaptive control techniques, we control the response system to be the drive system even though their orders are different and their parameters are unknown. The techniques are successfully applied to two examples: generalized Lorenz system (fourth order) and Lue system (third order); Roessler hyperchaotic system (fourth order) and Roessler system (third order). Furthermore, the effect of control modulator k is under our discussions