Memristor-Coupled Logistic Hyperchaotic Map

The continuous memristor models have been applied to various chaotic circuits. However, the discrete memristor models and their applications to discrete maps haven't attracted much attention, yet. In this brief, we first present a discrete memristor model and analyze its characteristics. By coupling the model into the Logistic map, a memristive Logistic map is further achieved. Due to the existence of line fixed point, the memristive Logistic map can be unstable or critically stable, depending on its control parameters and initial state. Using several analysis methods, we study the control parameters-relied dynamical behaviors of the memristive Logistic map and disclose its hyperchaotic attractors. The numerical results show that the discrete memristor can efficiently improve the chaos complexity in the Logistic map. In addition, digital experiments are designed to validate the numerical results.