Abstract: The hyperchaotic systems Kawakami map is synchronized completely using parametric adaptive control algorithm. After a rigorous mathematical deriving, a sufficient condition of the single-parameter adaptive control can be drawn for the synchronization of Kawakami map, and the synchronization is also found in double- parameter adaptive control. The simulation results show that the output signal of this map is similar to the spectrum of white noise, so it can he used in secret communication.

Key words: hyperchaos, weak chaos, parametric adaptive control algorithm, Lyapunov characteristic exponent, chaos synchronization, spectrum