Tri-Memristor Hyperchaotic Ring Neural Network With Hidden Firings: Dynamic Analysis, Hardware Implementation and Application to Image Encryption

The Hopfield neural network with unidirectional fixed resistance weights has been shown to exhibit limited complex dynamical behaviors due to its relatively simple architecture. To address this limitation, this paper proposes a new tri-memristor hyperchaotic ring neural network (THRNN). The THRNN facilitates the generation of hidden chaos and demonstrates homogeneous/heterogeneous multistability. Homogeneous coexisting attractors, when tightly connected across barriers, exhibit significant self-growth behavior over time. The number of growth directions can be freely regulated, and the multidirectional initial offset boosting characteristics of these growing attractors can also be readily observed. Furthermore, abundant hidden firing patterns are well-tuned by the coupling parameters of the memristors, resulting in chaotic bursting firing, periodic bursting firing, chaotic spiking firing, and periodic spiking firing. Particularly, a more complicated hidden hyperchaotic firing pattern is also discovered and captured. Moreover, an STM32H7 digital circuit is built to verify the findings presented in this paper. Finally, a hardware image blocking encryption system based on FPGA and the THRNN is proposed. This encryption system constructs a framework based on the hyperchaotic firing attractors and homogeneous multistability attractors. It realizes dynamic key update through block encryption strategy, and completes key scrambling by combining Cat mapping and sequence sorting, which significantly enhances encryption security. Relying on FPGA hardware implementation, its parallel processing capability greatly improves encryption efficiency, and the hardware deployment feature enhances the system’s stability and practicality, providing an efficient solution for high-security image encryption.