Basin Structure and Unpredictability in a Two-Dimensional Memristor-Based Cubic Map

This study investigates the dynamics of a two-dimensional memristor-based cubic map, with emphasis on the structure of its basins of attraction and the unpredictability of its long-term behavior. A recurrence-based automated method is employed to identify attractors without prior knowledge of their locations, which enables a comprehensive analysis of multistability. The resulting basin structures exhibit fractal boundaries and regions of divergence, reflecting a high sensitivity to initial conditions. To quantify the complexity of the attractor basins, basin entropy values are evaluated across various parameter sets as a measure of the system’s unpredictability. The results show regions of high basin entropy, which highlight the emergence of intricate fractal-like basin boundaries and robust chaotic behavior. These findings suggest that memristive elements can enhance complexity and unpredictability in discrete dynamical systems, with potential applications in the design of secure and resilient digital systems that exploit chaotic dynamics.