We present an approach to design spiking silicon neurons based on dynamical systems theory. Dynamical systems theory aids in choosing the appropriate level of abstraction, prescribing a neuron model with the desired dynamics while maintaining simplicity. Further, we provide a procedure to transform the prescribed equations into subthreshold current-mode circuits. We present a circuit design example, a positive-feedback integrate-and-fire neuron, fabricated in 0.25 μm CMOS. We analyze and characterize the circuit, and demonstrate that it can be configured to exhibit desired behaviors, including spike-frequency adaptation and two forms of bursting.