Nonparametric bifurcation mechanism in 2-D hyperchaotic discrete memristor-based map

Compared with continuous-time memristor (CM), discrete memristor (DM) has not been received adequate attention. In this paper, a new n-dimensional generalized DM model is proposed based on the discrete theory. Two 2-D discrete mathematical models satisfying the three fingerprints characteristics of memristors are designed. Applying the mathematical model into the Sine map yields a new hyperchaotic map called discrete memristor-based Sine (DM-S) map. The DM-S map has a line of fixed points, and its dynamical behaviors including nonparametric bifurcation and hyperchaos are explored by phase diagrams, bifurcation diagrams, and Lyapunov exponent spectrums. The i-v characteristics of the DM and the attractors of the DM-S map are implemented by digital signal processor. In addition, the sequences of map are tested by using SP800-22 NIST software.

Automated summary

A new n-dimensional generalized DM model is proposed in this paper based on discrete theory, along with two 2-D discrete mathematical models that satisfy the three characteristics of memristors. By applying the mathematical model to the Sine map, a new hyperchaotic map called DM-S is obtained. The dynamical behaviors of DM-S including nonparametric bifurcation and hyperchaos are explored through phase diagrams, bifurcation diagrams, and Lyapunov exponent spectrums.