Impulsively synchronizing chaotic systems with delay and applications to secure communication

In this paper, the presence of transmission delay and sampling delay in chaos-based secure communication systems by employing impulsive synchronization is studied. A time delayed impulsive differential system with delayed impulses, modeling the synchronization error between the driving and response schemes employed in such communication systems, is presented. The equi-attractivity property of the error dynamics is investigated and the sufficient conditions leading to this property are obtained. A set of upper bounds on the delay terms involved in the system are also obtained, and a numerical example is given. A communication security scheme employing hyperchaotic systems possessing continuous driving, impulsive driving and delay is proposed and simulation results are given to demonstrate the performance of the scheme. 2005 Elsevier Ltd. All rights reserved.