Two-Identical System Synchronization

In this chapter, the partial and full chaotic synchronizations of two nonlinear gyroscope systems with/without noise are investigated. From analytical conditions for synchronization and non-synchronization of two gyroscope systems, the parameter characteristic study is completed for a better understanding of the synchronization dynamics of two gyroscope dynamical systems. The boundaries of the parameter map for synchronization are determined by the onset and vanishing conditions of synchronization. The simple feedback control can make the noised gyroscope system synchronizing with chaotic behaviors of the expected gyroscope system. The methodology presented in this paper is different from other techniques for synchronization. The partial synchronization is an important phenomenon to be observed in engineering applications.