Abstract
Based on the classic Lorenz system, this paper studies the problem of bivariate module-phase synchronizations in a fractional-order Lorenz system, bivariate module-phase synchronizations in a fractional-order spatiotemporal coupled Lorenz system, and malposed module-phase synchronization in a fractional-order spatiotemporal coupled Lorenz system. It is the first time, to our knowledge, that module-phase synchronization in fractional-order high-dimensional 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 module-phase synchronization and malposed module-phase synchronization. The numerical simulation results demonstrate the validity of controllers.
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