Analysis of generalized projective synchronization for a chaotic gyroscope with a periodic gyroscope

► The generalized projective synchronization for two gyro systems is investigated. ► The theory of discontinuous dynamical systems is used in this paper. ► The necessary and sufficient conditions for such synchronization are developed. ► The synchronization invariant domain and the parameter maps are explored. ► The partial and full generalized projective synchronizations are carried out.