Reducible-dimension discrete memristive chaotic map

As research on chaotic maps based on discrete memristors advances, the chaotic map of multiple discrete memristors is gradually receiving attention. Therefore, this paper focuses on the parallel structure of multiple memristors and proposes a dimension-reduction method for such systems. The theoretical analysis of this method is validated by a novel reducible-dimension chaotic map based on the parallel structure of dual memristors. Numerical analysis reveals its reducible-dimension characteristics, two-dimensional degenerate attractor, and super-extreme multistability. Moreover, a pseudo-random number generator (PRNG) is designed using the map and the NIST SP800-22 test results show that the generated pseudo-random numbers have high randomness. The physical feasibility of the map is verified using the STM32 platform. Finally, an encryption strategy is proposed based on the degeneracy of this map, and multiple testing methods have verified the superior performance of the encryption system.