Dynamic analysis of high dimensional HNN with logistic-based memristors and application in military image encryption

In recent years, the use of memristors to build highly complex bionic neural network models is of great significance to the breakthrough of artificial intelligence technology. In this paper, a freely adjustable Logistic-based multistable memristor (LMM) is proposed, which has not been observed in previous studies of memristors. Easy adjustment of steady state and high response can be achieved by adjusting memory parameters. A high dimensional memristive hopfield neural network (LMMHNN) based on LMM is designed. Basic dynamics methods and numerical analysis tools are used to reveal the abundant discharge behaviors of LMMHNN. Multi-structure chaotic attractors generated by different coupling positions, hyperspatial attractors controlled by memory parameters and the coexistence of initial state-dependent hyperspatial attractors are observed. The isomorphic expansion behaviors of single chaotic attractors in one-dimensional plane, two-dimensional grid and three-dimensional space are observed. In addition, the hardware circuit corresponding to LMMHNN is designed. The reconstructed dynamic behaviors verify the feasibility of high dimensional memristive hopfield neural network. Finally, a military image encryption scheme based on LMMHNN combining double-bit DNA scrambling and dynamic matrix diffusion is proposed. A number of random test data show that the scheme performs well in resisting all kinds of analysis attacks, which has a wide application prospect in the field of military information security.