In this paper, the nonlinear dynamical phenomenon associated with a silicon neuron are described. The neuron has one transient sodium (activating and inactivating) channel and one activating potassium channel. These channels do not model specific equations; instead they directly mimic the desired voltage clamp responses. This allows us to create silicon structures that are very compact (six transistors and three capacitors) with activation and inactivation parameters being tuned by floating-gate (FG) transistors. Analysis of the bifurcation conditions allow us to identify regimes in the parameter space that are desirable for biasing the circuit. We show a subcritical Hopf-bifurcation which is characteristic of class 2 excitability in Hodgkin-Huxley (H-H) neurons. We also show a Hopf bifurcation at higher values of stimulating current, a phenomenon also observed in real neurons and termed excitation block. The phenomenon of post-inhibitory rebound and frequency preference are displayed and intuitive explanations based on the circuit are provided. The compactness and low-power nature of the circuit shall allow us to integrate a large number of these neurons on a chip to study complicated network behavior.