Synchronization of chaotic systems modulated by another chaotic system in an erbium-doped fiber dual-ring laser system

We show that two chaotic systems in erbium-doped fiber dual-ring lasers can be synchronized by using the output of one chaotic system (called the driving system) to modulate the parameters of the two systems. Numerical calculation shows that when the stiffness of modulation is properly adjusted, the two systems can he synchronized. Simultaneously, we find that when the driving system is in various periodic states, the two synchronized systems can go into periodic states.