Synchronizing hyperchaotic systems by observer design

Abstract

In this work, a technique for synchronizing hyperchaotic systems is presented. The basic idea is to make the driven system a linear observer for the state of the drive system. By developing this approach, a linear time-invariant synchronization error system is obtained, for which a necessary and sufficient condition is given in order to asymptotically stabilize its dynamics at the origin. The suggested tool proves to be effective and systematic in achieving global synchronization. It does not require either the computation of the Lyapunov exponents, or the initial conditions belonging to the same basin of attraction. Moreover, it guarantees synchronization of a wide class of hyperchaotic systems via a scalar signal. Finally, the proposed tool is utilized to design a secure communications scheme, which combines conventional cryptographic methods and synchronization of hyperchaotic systems. The utilization of both cryptography and hyperchaos seems to make a contribution to the development of communication systems with higher security.