Hidden attractors in fractional-order discrete maps

Abstract

This study investigates the hidden dynamics of fractional-order discrete two-dimensional maps, focusing on the generation of hidden attractors and the impact of order on their size and boundaries. Three different nonlinear maps are used, and various measures, such as phase portraits, bifurcation diagrams, and basin of attraction, are presented. This study also observes changes in basin boundaries of hidden attractors with varying order. The rational memristive maps exhibit a well-defined basin of attraction for a broad range of system orders, with multistability and a riddled basin for some orders. The memristive Gauss map also shows well-defined and riddled basins, however, the quadratic chaotic map demonstrates a decreasing basin size and a riddled basin boundary for higher orders of the system.