Construction and implementation of discrete memristive hyperchaotic map with hidden attractors and self-excited attractors

Abstract

The investigation of discrete memristor and its application in the discrete map is valuable and meaningful. This paper proposes a new one-dimensional map and couples it with a discrete memristor to construct a memristive hyperchaotic map. The most distinctive feature of this map is that it can generate self-excited and hidden chaotic attractor (HCA), the coexistence dynamics of these two types of attractors are different under the conditions of their generations. The relationship between the fixed points and the parameters is analyzed, revealing that it has line fixed points or no fixed points. Moreover, due to the introduction of the memristor, it has a more extensive chaotic range than the original map and can generate hyperchaotic attractors (HA) with better performance metrics. Finally, the map is implemented in a digital circuit to verify the experimental results.