Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

A new synchronization scheme for chaotic (hyperchaotic) maps with different dimensions is presented. Specifically, given a drive system map with dimension n and a response system with dimension m, the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states. The method, based on the Lyapunov stability theory and the pole placement technique, presents some useful features: (i) it enables synchronization to be achieved for both cases of n < m and n > m; (ii) it is rigorous, being based on theorems; (iii) it can be readily applied to any chaotic (hyperchaotic) maps defined to date. Finally, the capability of the approach is illustrated by synchronization examples between the two-dimensional Henon map (as the drive system) and the three-dimensional hyperchaotic Wang map (as the response system), and the three-dimensional Henon-like map (as the drive system) and the two-dimensional Lorenz discrete-time system (as the response system).