Expanded Lorenz systems and chaotic secure communication systems design

Using Lyapunov theory, the Lorenz chaotic system was partitioned in two parts, where one of them is globally asymptotically stable. This partition facilitated the state-space expansion of the Lorenz system from three to four-order. This new four-order Lorenz system, one of its states is synchronized with other. This expansion allows us to design a secure communication system where the dynamic of the receiver is just one-order. The proposed secure communication system uses two-lines of transmission. Simulation results are included to demonstrate the performance of this secure communication system based on this new four-order Lorenz system.