Synchronization of chaotic erbium-doped fiber dual-ring lasers by using the method of another chaotic system to drive them.

A method of chaotic synchronization is presented in this paper that uses the chaotic output of one system to drive two other identical chaotic systems. The criterion is defined that, when the maximum conditional Lyapunov exponents (MCLE's) of the two systems are negative, the two systems can be synchronized to each other. As a possible application we numerically investigated the synchronization of chaotic erbium-doped fiber dual-ring laser systems. Numerical calculation shows that when driven by another chaotic system, if the two identical systems are in chaos and their MCLE's, are negative, they can go into chaotic synchronization whether or not they were in chaotic states previously. Simultaneously, we find that the states of the two systems vary with that of the driving system. When the driving system is in different periodic states, the two systems can still retain synchronization and go into corresponding different periodic states.