Grid Homogeneous Coexisting Hyperchaos and Hardware Encryption for 2-D HNN-Like Map

Compared with the continuous Hopfield neural network (HNN), the discrete HNN remains relatively under-explored in both academic and industrial domains. This paper proposes a simple two-dimensional (2-D) HNN-like map for neurons with specific internal decay. It is a discrete map with an infinite number of grid unstable points, leading to the appearance of grid homogeneous coexisting attractors. Theoretical analysis deduces the switching mechanism of initial-offsets, while numerical simulations disclose the grid homogeneous coexisting bifurcation behaviors and hyperchaotic attractors. The results manifest that 2-D HNN-like map can exhibit grid homogeneous coexisting hyperchaos in two dimensions and the highly random hyperchaotic sequences can be losslessly switched by two initial values. Additionally, hardware implementation on an STM32 platform validates the coexisting hyperchaotic attractors. Furthermore, using the initials-switched grid homogeneous coexisting hyperchaotic sequences, we develop a reliable and secure geolocation-based chaotic hardware encryptor. To our best knowledge, this is the first application of grid homogeneous coexisting hyperchaos in industrial field.