The non-capacitor model of leaky integrate-and-fire $VO_2$ neuron with the thermal mechanism of the membrane potential

The study presents a numerical model of leaky integrate-and-fire neuron created on the basis of $VO_2$ switch. The analogue of the membrane potential in the model is the temperature of the switch channel, and the action potential from neighbouring neurons propagates along the substrate in the form of thermal pulses. We simulated the operation of three neurons and demonstrated that the total effect happens due to interference of thermal waves in the region of the neuron switching channel. The thermal mechanism of the threshold function operates due to the effect of electrical switching, and the magnitude (temperature) of the threshold can vary by external voltage. The neuron circuit does not contain capacitor, making it possible to produce a network with a high density of components, and has the potential for 3D integration due to the thermal mechanism of neurons interaction.