We analyze the dynamics of insulator-metal transition (IMT) based neurons, through material-device co-design and optimization. We explore the correlation between the membrane potential and the bias voltage for the resistance stack of the IMT neuron. For a set of nominal parameters, we show that a minimum bias voltage of ~300 mV and a minimum gate input of ~400 mV is required to ensure oscillatory behavior in the IMT neuron. These biasing constraints can be slightly relaxed by increasing the size of the auxiliary transistor. A 4X increase in the transistor width can only lead to ~ 80 mV increase in the window of oscillatory operation with a ~3.8X increase in the current through the neuron. For low power operation, it is optimum to use minimum sized transistor with more than 400 mV of membrane and bias voltages. Analyzing the implications of the material parameters, we report that, the trigger voltage (VTRIG) of the neuron can be linearly tuned by choosing appropriate critical voltage for IMT switching. The insulating state resistance (RINS) also plays a role in determining the VTRIG. But, to reduce the VTRIG by 50 mV, the RINS needs to be lowered by ~5X. For RINS <150 KΩ and metallic state resistance (RMET) < 700 Ω, it is possible to operate the neuron in a special bi-stable oscillatory mode (avoiding the metastable operation). But if the width of transistor is lower (NFIN < 4), only metastable oscillation is possible. The frequency of oscillation is coupled to the transistor resistance and ~25 mV reduction in threshold voltage (VTH) leads to >15% increase in the frequency. We perform 10,000 Monte-Carlo simulations (3) to analyze the effect of variation on this neuron topology. Considering Gaussian distribution in the VTH and in all the parameters of the IMT material, we calculate ~150 mV of spread in the values of the VTRIG. The variation induced spread is not sensitive to the transistor size. That indicates the possibility of using a minimum sized transistor, without affecting the degree of variation tolerance of the neuron.