Theory and experimental realization of observer-based discrete-time hyperchaos synchronization

Research in the synchronization of dynamical systems has been mainly focused on chaotic rather than hyperchaotic systems and on continuous-time rather than discrete-time systems. Numerical simulations dominate these studies and results typically lack experimental data. This brief fills these gaps by 1) presenting a technique for the exact (dead-beat) synchronization of hyperchaotic discrete-time systems; and 2) describing an electronic implementation of this technique for the generalized Henon map. The synchronization strategy is based on the observer concept and enables a wide class of hyperchaotic discrete-time systems to be synchronized via a scalar signal. An electronic implementation provides verification of the theoretical results and confirms the feasibility of realizing this approach in hardware.