Dimensionality Reduction Analysis for Detecting Initial Effects on Synchronization of Memristor-Coupled System

This paper presents a 9-D memristor-coupled system with three ideal memristors and investigates its initial effects on synchronization using dimensionality reduction analysis method. The 9-D memristor-coupled system is yielded from two identical 4-D ideal memristor-based hyper-jerk systems via coupling an ideal memristor, from which the initials-dependent synchronization with parallel offset for larger coupling strength is numerically exhibited. To explore the initial effects on synchronization, an equivalent 6-D dimensionality reduction model is built using state variable mapping (SVM) method, from which the implicit initials of the 9-D memristor-coupled system are transformed into the explicitly initials-related system parameters of such a 6-D dimensionality reduction model. Thus, the inherent initial mismatches between the two coupled identical 4-D subsystems are explicitly expressed as the initials-related parameter mismatches between the two coupled non-identical 3-D dimensionality reduction subsystems. The initials-related boundedness of the error system between the two non-identical 3-D dimensionality reduction subsystems is derived by Lyapunov analysis method, upon which the initial effects on synchronization with parallel offset are expounded quantitatively. Furthermore, the initials-dependent synchronization is well confirmed by the numerical simulations, which demonstrates that the initials do have great influence on synchronization dynamics of the coupled memristive system.