Analysis and synthesis of synchronous periodic and chaotic systems

Chaotic systems are known for their sensitivity to initial conditions. However, Pecora and Carroll [Phys. Rev. Lett. 64, 821 (1990); Phys. Rev. A 44, 2374 (1991); IEEE Trans. Circuits Syst. 38, 453 (1991)] have recently shown that a system, consisting of two Lorenz oscillators exhibiting chaos, could achieve synchronization if a portion of the second system is driven by the first. In this paper, a necessary and sufficient condition for synchronization is presented. This condition has been used to create a high-dimensional chaotic system with a nonlinear subsystem. This system shows synchronization both when it exhibits periodic limit cycles and when it turns chaotic.