Design of a novel memristor-modulated hyperchaotic map with differential variable input

Chaos performance enhancement techniques have emerged as one of the pivotal research focal points in the realm of nonlinear physics. By inputting the differences of state variables into the seed fraction map (FM) and coupling it with a discrete memristor, a novel state variable difference input memristive fraction map (DMFM) is constructed in this paper. The presence of infinite fixed points unveils the multi-stability of DMFM, and simulation experiments demonstrate the coexistence of multiple attractors, highlighting the high sensitivity to initial conditions. Bifurcation diagrams reveal the reduction of the number of periodic windows for the seed map after difference input and memristor modulation. The hyperchaotic state within certain parameter ranges is verified by the Lyapunov exponent spectrum. Moreover, the broadening of the chaos interval further substantiates that the use of state variable difference input and the modulation of memristor effectively enhance the chaotic performance. The initial-boosting behavior of DMFM exhibits complex dynamics. Regarding practical applications, a pseudo-random number generator based on DMFM is designed and successfully passed the TestU01 and NIST SP800-22 tests. The digital signal processing (DSP) implementation of the system lays an experimental foundation for its application.