Gated Memristive Coupling in a Hindmarsh-Rose Neural Network: Nonlinear Dynamics and Hardware Implementation

Inspired by astrocyte-mediated modulation in tripartite synapses, this study proposes a gated memristive coupling mechanism for neural networks. Unlike conventional pairwise coupling scheme with predefined interaction strengths, the proposed framework introduces an independent neuronal state to regulate the evolution of the gated memristive element's state variable, forming a dynamic modulation pathway. Through this mechanism, the coupling strength between two neurons can be continuously adjusted by the activity of a third neuron without directly modifying the intrinsic coupling coefficients. A three-neuron Hindmarsh-Rose network with gated memristive coupling channels is constructed to investigate the resulting nonlinear dynamics. Bifurcation analysis, Lyapunov exponents, and two-parameter maps reveal that the proposed architecture generates diverse transitions among periodic, multi-periodic, and chaotic firing regimes. Different coupling channels exhibit distinct regulatory characteristics, and their interaction produces complex distributions of dynamical regions in the parameter space. Furthermore, external excitation analysis demonstrates that neuronal inputs provide an additional control pathway by modulating the membrane potential of the gating neuron, thereby indirectly regulating the effective coupling strength. The feasibility of the proposed mechanism is validated through real-time digital signal processor (DSP) implementation, where hardware-generated trajectories agree well with numerical simulations. This work provides a compact and hardware-realizable framework for studying state-dependent neural coupling regulation and offers a potential approach for adaptive neuromorphic systems.