Design and analysis of a three-dimensional discrete memristive chaotic map with infinitely wide parameter range

Abstract

In this paper, a new discrete memristive chaotic map with infinitely wide parameter range is designed. Firstly, a discrete memristor based on a triangular wave function is constructed. The memristor conforms to the definition of generalized memristor, and a new three-dimensional memristive chaotic map is designed based on it. Numerical simulations show that the map has complex dynamic behavior. An improved perturbation method is proposed to estimate the output sequence of the chaotic system. At the same time, it is proved mathematically that the new map can always be in chaotic or hyperchaotic state with infinitely wide parameter range under certain conditions. By observing the Lyapunov exponent spectrum and the phase diagram, it is found as the absolute value of the parameter increases, the output range and ergodicity of the new map are also enhanced. We demonstrate that the new map has an initial-boosting behavior that depends on the initial conditions of the memristor. By changing the initial values of the memristor, we can control the appearance of attractor at different locations without loss. At the same time, this paper analyzes the mechanism of the discrete memristive chaotic map generating initial-boosting behavior, puts forward a method to make ordinary chaotic maps easier to obtain this behavior. Finally, the DSP hardware platform is used to implement the new map, which proves the physical existence and realizability of the map.