<p>To explore the connection between the bistable characteristics and neuromorphic characteristics of memristors and enrich neuromorphic behaviors, a novel bistable locally active memristor is proposed. By analyzing the two mechanisms of the memristor switching from negative to positive stable state, a third-order neuron circuit was designed. Based on the Edge of Chaos (EoC) criterion, the generation mechanisms of neuromorphic dynamics under different stable states were analyzed. The results show that under the positive stable state, the neuron circuit always has a larger Right Half Plane (RHP) domain and can generate dissipative chaotic attractors. Abundant coexisting behaviors are observed near the EoC, and the basin of attraction of the negative stable state shows a negative correlation with the input voltage. Interestingly, through the stable state switching mechanisms of the memristor, it is demonstrated that neurons near the EoC can also achieve the switching of action potentials, such as periodic-to-periodic, chaotic-to-periodic, resting-to-chaotic, and resting-to-periodic spiking. It reproduces bistable switching behaviors similar to those of biological neurons, can be successfully applied to neural network pattern recognition, and demonstrates 24 types of neuromorphic behaviors near the EoC. Finally, the switching behaviors of the action potentials of the neuron circuit is reproduced using the hardware circuit designed with Field-Programmable Gate Array (FPGA), thereby verifying the feasibility of the proposed model.</p>