New feedback functions for synchronizing chaotic maps

Abstract

Synchronization of chaotic maps is studied using the method of variable feedback. A general method is presented for generating feedback functions for maps. These feedback functions are found very efficient. Our study shows that when the driver and the response systems are fed by common noise, the noise does not affect synchronization. With different but weak noise added to the driver and response systems, approximate synchronization persists. [7] observed that two initially different trajectories of a chaotic attractor fed by common noise coalesce when calculations are carried out with finite precision. Lech et al.[8] and Pikovsky [9] have shown that if the calculations are done with higher precision the coalescence time -(for maps -=no. of iterations) increases exponentially and the procedure soon becomes practically impossible to implement. Clearly, the application of common noise for synchronization of chaotic attractors has inherent difficulties. In this work we will see that synchronization of chaotic attractors in the presence of common noise poses no additional difficulty [2].