We present a circuit architecture for compact analog VLSI implementation of the Izhikevich neuron model, which efficiently describes a wide variety of neuron spiking and bursting dynamics using two state variables and four adjustable parameters. Log-domain circuit design utilizing MOS transistors in subthreshold results in high energy efficiency, with less than 1pJ of energy consumed per spike. We also discuss the effects of parameter variations on the dynamics of the equations, and present simulation results that replicate several types of neural dynamics. The low power operation and compact analog VLSI realization make the architecture suitable for human-machine interface applications in neural prostheses and implantable bioelectronics, as well as large-scale neural emulation tools for computational neuroscience.