Neuromorphic computing uses spike neurons for parallel processing, which can overcome limitations of digital computers, thereby improving computing speed, performance, and energy efficiency to achieve more efficient, intelligent, and adaptive computing. The ultrafast Kerr effect has important significance and application in neuromorphic computing. An improved coupled mode theory (CMT) model was employed to analyzed the nonlinear dynamics behaviors in a micro-resonator based on the ultra-fast Kerr response of perovskite materials. Self-pulsation behavior was observed in the optical cavity. Based on this property, the excitation, leaky integrating dynamics and refractory time of optical neurons were simulated and implemented. Because of the ultra-fast Kerr response of the perovskite material, the refractory time of the optical neuron can be reduced to the order of picoseconds, which paves the way for ultra-fast spiking neural networks.