Bivariate Module Phase Synchronization of a Fractional Order Lorenz System in Different Dimensions

Abstract

Based on the classic Lorenz system, this paper studies the problem of bivariate modulephase synchronizations in a fractionalorder Lorenz system, bivariate modulephase synchronizations in a fractionalorder spatiotemporal coupled Lorenz system, and malposed modulephase synchronization in a fractionalorder spatiotemporal coupled Lorenz system. It is the first time, to our knowledge, that modulephase synchronization in fractionalorder highdimensional systems is applied. According to the fractional calculus techniques and spatiotemporal theory, we design controllers and achieve synchronizations both in module space and phase space at the same time. In the simulation, we discuss the bivariate modulephase synchronization and malposed modulephase synchronization. The numerical simulation results demonstrate the validity of controllers.