Design of a discrete memristive chaotic map: fractional-order memory, dynamics and application

In this paper, a discrete fracmemristor (DFM) model is derived based on the Caputo difference, and a new fractional-order chaotic map is designed. Dynamics of the proposed map is investigated in detail by means of Lyapunov exponent spectra, bifurcation diagrams, PE complexity and multistability analyses. Compared with the coupled discrete integer-order memristor (DIM), the map coupled with the DFM products richer dynamics, including larger attractor distribution, fewer numerically periodic windows, and higher complexity. Besides, the order becomes additional bifurcation parameter. Finally, the proposed map is implemented on Field-Programmable Gate Array (FPGA) platform, and applied in a pseudorandom number generator (PRNG), which further demonstrates its application value.