Synchronization of fractional chaotic and hyperchaotic systems using an extended active control

Abstract

An extended active control technique is used to synchronize fractional order chaotic and hyperchaotic systems with and without delay. The coupling strength is set to the value less than one to achieve the complete synchronization more easily. Explicit formula for the error matrix is also proposed in this chapter. Numerical examples are given for the fractional order chaotic Liu system, hyperchaotic new system and Ucar delay system. The effect of fractional order and coupling strength on the synchronization time is studied for non-delayed cases. It is observed that the synchronization time decreases with increase in fractional order as well as with increase in coupling strength for the Liu system. For the new system, the synchronization time decreases with increase in fractional order as well as with decrease in coupling strength.