A DISCRETE MEMRISTOR COUPLED TWO-DIMENSIONAL GENERALIZED SQUARE HYPERCHAOTIC MAPS

Abstract

In this paper, a new discrete chaotic map is constructed by introducing a discrete memristor in two-dimensional generalized square maps to enhance its chaotic performance. First, the fixed points of the new maps are analyzed, and the effects of different parameters on the system performance are investigated by bifurcation diagrams, Lyapunov exponential spectra and phase diagrams. Second, the fixed points of the new maps are analyzed, and the effects of different parameters on the system performance are investigated by bifurcation diagrams, Lyapunov exponential spectra and phase diagrams. The distinctive characteristic of a discrete system is the coexistence of various types of attractors, and there is coexistence of hyperchaos and cycles in the present maps. It is worth mentioning that symmetric chaotic attractors with different positive and negative parameters are found during the study. In addition, the phenomenon of state transition between chaos and cycles is also found. Finally, the discrete maps are designed and implemented using a DSP platform. The results of the study provide a reference for the application of discrete amnesic chaotic maps.