<p>Biphasic action potentials represent a critical neuromorphic behavior of biological neurons. It is a prominent challenge to generate biphasic action potentials based on the memristor characteristics since the generation mechanisms of biphasic action potentials remain unclear. A novel locally active memristor with symmetrical stable states (SS-LAM) is proposed to investigate the connection between the generation of biphasic action potentials in the memristive neuron circuit and the mermistor’s characteristics of the symmetrical stable state. Theoretical analysis based on the local activity theory and the edge of chaos (EOC) criterion reveal the physical origin of biphasic neuromorphic behaviors in a neuron circuit with the SS-LAM. The results indicate that the neuron circuit based on the SS-LAM not only retains the device’s local activity and DC V-I characteristics but also inherits its bistability. The symmetrical stable state behaviors of the SS-LAM give rise to symmetrical locally active domains, enabling the neuron to generate various monophasic and biphasic action potentials near the EOC through Hopf bifurcation. These include rich dynamic behaviors such as periodic spiking, bursting, adaptation, as well as chaotic oscillations and bistability induced by aberrant neuronal firing. Finally, an FPGA-based implementation of the neuron circuit is presented. The experimental results agree with the numerical simulations, verifying the feasibility of the proposed artificial neuron model.</p>