Dynamics and Synchronization in a LAM-Coupled Neuron Network

Complex neuronal dynamics arising from adaptive synapses are fundamental to both biological brains and neuromorphic systems. This paper studies the nonlinear dynamics of a Bi-Hindmarsh–Rose (bi-HR) neuron network coupled via a Locally Active Memristor (LAM) synapse. By introducing a flux-controlled LAM as an adaptive coupling element, a five-dimensional memristive neuronal system is constructed and analyzed. Equilibrium and stability analyses reveal intrinsic instability induced by memristive local activity. Numerical results demonstrate rich dynamical behaviors, including quasi-periodic states, chaos, bursting discharge, and synchronization with strong dependence on the coupling strength, external bias current, and memristor initial states. Under sinusoidal excitation, bursting discharge patterns are observed and their formation mechanism is clarified through bifurcation analysis. Sufficient conditions for exponential synchronization are derived, and extreme sensitivity of synchronization to the memristor state is verified. FPGA implementation further validates the observed dynamics and enables high-quality chaotic signal generation. These results highlight the potential of locally active memristive synapses for neuromorphic and hardware-oriented applications.