Reduced order anti-synchronization between single mode laserLorenz system and Duffing system

A controller was designed with the active control method to realize the reduced order anti-synchronization between a 2-order Duffing system and a 3-order single-model laser Lorenz system. Based on Routh-Hurwitz criteria, the conditions for the error dynamic system to be asymptotically stablized at the origin were given. The numerical experiments verify that the state variables of the 2-order Duffing system and the projection subsystem of the 3-order singlemodel laser Lorenz system vibrate with the same amplitude but opposite direction when the designed controller is used. The anti-synchronization is achieved under random noise interference. It proves that the designed controller is feasible and effective, and has better robustness for achieving the reduced order anti-synchronization between different order Duffing system and Lorenz system.