SNNAP, the Simulator of Neuronal Nets and Action Potentials, uses Hodgkin-Huxley type differential equations to simulate a cell's conductances that in turn may be modulated by second messengers or ion pools. SNNAP can simulate networks of up to 100 cells and 300 electrical, chemical and modulatory synaptic. Time dependent synaptic conductances are described by second-order ordinary differential equations. The experimenter can then perform virtual elektrophysiological experiments or observe the net's spontaneous behavior.

I can provide a brief SNNAP text overview or a colorful poster with the title "Simulating Physiological and morphological Properties of Neurons with SNNAP (Simulator for Neural Networks and Action Potentials)". Download the abstract in HTML or the poster in PDF.

My first successful simulation was a network of two identical neurons that exhibit postinhibitory rebound firing, i.e. they fire after they have been hyperpolarized. To do this I equipped the cells with a non-deactivating, cation driven inward rectifier, that activates upon hyperpolarization: the "h current". Both cells are connected to each other by an inhibitory synapse, i.e. cell A fires and inhibites (hyperpolarizes) cell B and if cell B fires it inhibits cell A. Obviously, this leads to rhythmic alternating firing if one of the cells if briefly hyperpolarized by injecting negative current:

(click on image to enlarge)

Interestingly, it was possible to adjust synaptic strength, the time constant of the synaptic current and the h-current so that the number of spikes would be proportional to the intensity (duration or Amperage) of the stimulating current:

In this run of the simulation, the current was chosen such that the cells would alternatingly fire single spikes. Of course these simulations only reflect the behavior of potentially 'real' cells. None of the values have been adjusted to match any particular biologically meaningful data. The cells simulated here are purely hypothetical.