<p>Existing research has predominantly focused on neuronal networks composed solely of neurons, with limited exploration into the effects of neuron–astrocyte interactions. Current analyses of neuron–astrocyte network mechanisms often involve complex interactions that integrate both chemical and electrical signaling, making it challenging to fully understand brain function. Memristors have been extensively studied for their ability to emulate biological synapses. However, astrocyte heterogeneity and variations in memristor parameters require further detailed investigation, particularly regarding their impacts on neuronal firing, which remain poorly understood. To address these gaps, this study introduces a liquid memristor as a biomimetic synapse to replicate the environment and the combined electrical and chemical synaptic effects observed in biological synapses. Subsequently, a novel neuron–astrocyte network incorporating such a memristor synapse is constructed, and comprehensive numerical simulations are conducted. The results reveal that increased coupling strength and enhanced astrocyte regulatory feedback modulate firing dynamics and facilitate neuronal synchronization. Importantly, astrocyte heterogeneity exerts a significant influence on firing activities but has a negligible effect on synchronization. Conversely, variations in memristor parameters substantially affect both the transition and synchronization of neuronal firing activities. Ultimately, a neuron–astrocyte coupling circuit utilizing current-mode devices is designed to validate the theoretical results and demonstrate their physical feasibility.</p>