Design and Implementation of a New Hyperchaotic Memristive Map

The two-dimensional (2D) discrete maps with complicated dynamics have lately received a lot of interest. However, the discrete enhanced 1D map models and their combinations with memristors haven’t received much attention. In this brief, we first present an enhanced 1D map with more significant chaotic characteristics. By coupling a discrete memristor into the enhanced map, a novel 2D memristive map with infinite fixed points is further proposed. We also study the map’s parameter-relied dynamical behaviors and multi-stability phenomena using various analysis methods and demonstrate its hyperchaos and coexisting attractors. The numerical results show that the addition of a memristor boosts the map’s chaotic complexity. Digital experiments based on a microcomputer are also shown, with results that are consistent with the numerical analysis.