Synchronization of chaotic maps by feedback control and application to secure communications using chaotic neural networks

In this paper we propose a method to synchronize chaotic maps by feedback control. This approach is particularly attractive, if it can be made to work on a wide variety of chaotic systems, because it requires very little computational overhead and so is extremely easy to implement in fast hardware. In general the control feedback used here makes use of a diagonal matrix with experimentally determined components. However, for this particular application, synchronization is achieved by using only one element of the feedback matrix. To demonstrate the method we first apply it to the Henon map and study the local stability properties. We next apply the method to a neural network approximation of the Ikeda system and show that two identical copies of this network can be easily synchronized. The ability to synchronize two identical neural network approximations of a given chaotic system has potentially interesting applications in secure communications. In the final section we demonstrate how messages can be encoded, transmitted and decoded using the Ikeda neural network in combination with the feedback control method.