Modeling different discrete memristive sine maps and its parameter identification

Abstract

Compared with the continuous chaotic system designed by analog circuit, chaotic maps realized by the digital circuit has the characteristics of simple logic and easy implementation, so it has attracted more attention in engineering applications. How to construct the chaotic map with simple structure and strong complexity behaviors has always been a research hotspot. Recently, the concept of discrete memristor receives growing discussion. Existing studies have found that introducing it into classical chaotic map can enhance its chaotic characteristics. In this paper, three discrete memristor mathematical models are summarized. These models are introduced into the classical sine map, and three new two-dimensional discrete memristive sine maps are constructed. Dynamic analysis demonstrate the effect of the discrete memristor in improving the chaos characteristics. The proposed new systems not only expand the scope of chaos, but also greatly improve the Lyapunov exponent value, and appear hyperchaotic behavior and coexisting attractors. Through the parameter identification technology, the proposed discrete memristive chaotic maps are compared with several existing chaotic maps. The identification simulations show that the proposed chaotic maps have lower identification rate, so their security is higher.