A class of novel discrete memristive chaotic map

Abstract

Since Chua introduced the memristor as the fourth basic circuit component, memristors and memristive chaotic maps have received great attention. In this paper, we present a class of novel memristive chaotic map by coupling the discrete memristor with the internal item in an original boundary function. Several examples are presented based on classical one dimensional (1D) and high dimensional (HD) chaotic maps, and numerical simulation results display their improved dynamical performance and chaos complexity. We analyze the influences of introducing the memristor on the chaotic map and the generality for designing discrete chaotic maps of the proposed memristive model. Particularly, with the newly emerging features of no fixed points and multistability, we can robustly control the output sequence by setting their initial-states, which accommodates to many arisen applications of chaotic systems. Furthermore, based on the proposed memristive chaotic map, we construct the hardware platform to acquire its attractors, and design the Pseudorandom Number Generator (PRNG) to explore its application prospects.