<p>The Spiking Neural Network (SNN), emulating the brain’s operational principles, has demonstrated significant theoretical and experimental promise. However, it confronts several challenges, including underdeveloped training algorithms, substantial computational power requirements, a scarcity of benchmark datasets, and issues related to network scalability. Consequently, the development of novel models for these networks is imperative. This paper introduces a novel discrete spiking neuron model, which incorporates discrete memristor synapses, to explore neural firing mechanisms. In contrast to traditional continuous models governed by differential equations, our methodology establishes a fully discrete framework by integrating the discrete Chialvo neuron with the proposed spiking neuron, which is represented as a discrete map. The firing mechanism of the proposed spiking neuron is analyzed, revealing that the synaptic weight and neuronal firing pattern are determined by the input spikes. Furthermore, the learning capacity of a single neuron and Spike-Timing-Dependent Plasticity are discussed, highlighting the potential application value within the realm of artificial intelligence and establishing a foundation for additional research into the design of discrete spiking neural networks.</p>