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.