Modified projective synchronization of chaotic dissipative gyroscope systems via backstepping control

This paper proposes the modified projective synchronization for heavy symmetric dissipative gyroscope systems via backstepping control. Because of the nonlinear terms of the gyroscope system, the system exhibits complex and chaotic motions. Using the backstepping control technique, control laws are established which guarantees the hybrid projective synchronization including synchronization, anti-synchronization and projective synchronization. By Lyapunov stability theory, control laws are proposed to ensure the stability of the controlled closed-loop. Numerical simulations are presented to verify the proposed synchronization approach. This paper demonstrates that synchronization and anti-synchronization can coexist in dissipative gyroscope systems via nonlinear control.