The dynamic and discrete systems of variable fractional order in the sense of the Lozi structure map

Abstract

The variable fractional Lozi map (VFLM) and the variable fractional flow map are two separate systems that we propose in this inquiry. We study several key dynamics of these maps. We also investigate the sufficient and necessary requirements for the stability and asymptotic stability of the variable fractional dynamic systems. As a result, we provide VFLM with the necessary criteria to produce stable and asymptotically stable zero solutions. Furthermore, we propose a combination of these maps in control rules intended to stabilize the system. In this analysis, we take the 1D-and 2D-controller laws as givens.