Constructing multi-cavity attractors in discrete Hopfield neural system via pulse control

Neural functions are intrinsically linked to complex dynamical behaviors, where the topological diversity of attractors reflects the richness of potential neural states. The multi-scroll attractors in continuous neural networks have been extensively studied, while constructing distributed multi-cavity attractors in discrete neural systems remains a challenge. This paper investigates a discrete Hopfield neural system with a sine function as the activation function, which exhibits the phenomenon of grid coexisting attractors. To connect these independent coexisting attractors and make them a multi-cavity attractor, a pulse control scheme is introduced to reconfigure the topological structure of the system phase diagram. By designing the programmable pulse controller, trajectories can be transformed between previously separated coexisting attractors in the expected order, allowing for deterministic construction of N×M grid multi-cavity attractors. The dynamical analysis of Lyapunov exponent spectra (LEs) and permutation entropy (PE) complexity shows that the discrete Hopfield neural systems with multi-cavity attractors have higher complexity compared to those with single-cavity attractors. The experiment result based on digital signal processor (DSP) is consistent with that of the numerical simulation, verifying the physical feasibility of the proposed discrete multi-cavity neural system and providing a foundation for complex information processing and engineering applications.