Bifurcations in a silicon neuron

In this paper, we describe the bifurcations occurring in a silicon neuron with one sodium and one potassium channel. The channels are designed to model the physics of ion flow in actual biological channels instead of modeling a particular set of equations. We show a pair of subcritical Hopf-bifurcation with increase in current stimulus which is characteristic of class 2 excitability in Hodgkin-Huxley neurons. Theoretical analysis of the bifurcations lead to conditions for designing and biasing the circuit. The circuit is very compact, comprising six transistors and three capacitors, lending itself to easy integration. The parameters are set using floating-gate transistors and can be programmed as desired. We hope to study more complicated dynamics of large networks of these neurons, a task which might be beyond a typical digital computer.