This work shows the simulation of a CMOS spiking neuron model that can mimic the behaviour of a biological neuron for both hyperpolarizing and depolarizing currents. The proposed schematic design can exhibit the post-inhibitory rebound excitation (PIRE) or anode break excitation (ABE) phenomena. The model has multiple control parameters for regulating the operation of a neuron. It is shown that the electrophysiological properties of a neuron, such as spiking frequency, spike height, resting potential, and mean inter-spike interval, can be varied by adjusting two control parameters of the developed schematic. Schematic of excitatory and inhibitory synapses to link two neuronal models are designed using CMOS. Average power dissipation and energy consumed per spike of the schematic designs are examined. Furthermore, PIRE is demonstrated for a strong inhibitory synaptic current. The significance of including PIRE in such a neuronal model is shown by its necessity in the generation of persistent activity in the network, which mimics the realization of working memory or attention. A network of such neuronal designs with the appropriate realization of the synaptic region has implications for human-to-machine interfaces and pattern recognition problems