A new dynamic synchronization method to different random initial-times master-response real order systems

Going beyond nonlinear master-response real-order systems with distinct random initial times has been a long-standing open problem, and it is not known how to synchronize dynamics between them. This article demonstrates memory chaos synchronization between two different real-order systems associated with distinct random initial times, employing a new method. A new dynamic equation with an external order subject to a designed nonlinear control law has been implemented to establish some new theoretical conditions that guarantee dynamic asymptotic synchronization, and Mittag-Leffler asymptotic synchronization is put forward. Random initial-time real-order Chua’s system and Li and Sprott systems are considered to illustrate the importance of the proposed method, including simulations.