Multi-mechanism driven geometric control of discrete memristive dual-neuron HNN: Modulation analysis and hardware implementation

In recent years, the dynamical modulation mechanisms of discrete memristive Hopfield neural networks (HNNs) have received much attention. In this paper, a four-dimensional discrete Hopfield neural network model (4DMCHNN) based on the crosstalk effect of memristive synapses is proposed. This work systematically investigates the complex dynamical regulatory behaviors emerging in neural network architectures with synaptic crosstalk, revealing how different regulatory mechanisms influence the system’s chaotic properties. Analysis indicates that the system exhibits a rich variety of chaotic phenomena: amplitude control primarily depends on synaptic crosstalk intensity and internal memristor parameters; periodic dynamic modulation is dominated by memristor parameters, while the regulatory capability of the self-coupling weight on attractor offset has been improved. Furthermore, the system exhibits initial-value-induced shifts and the numerically verified coexistence of homogeneous attractors. Finally, the 4DMCHNN is implemented on a digital circuit platform, and a pseudo-random number generator constructed from its output successfully passes the NIST statistical tests. Low-cost hardware implementations drive neuromorphism toward practical applications. The investigation of predictably modulated chaotic behaviors in neural network systems, thus, offers new tools for modeling neurological diseases and implementing chaos control.