It seems logical to start building a neural network framework or a simulator with a neuronal model. Neuronal models and their implementations range from simple (like the model that is implemented in Neural Viewer) to very complex (like the Hodgkin-Huxley model). While there are many models to use (Which model to use for cortical spiking neurons? [?] article provides a good coverage of the existing models) I like the model proposed by Eugene Izhikevich in Simple model of Spiking Neurons [?] as it is computationally efficient and still biologically plausible.
Eugene's website provides MATLAB scripts to play with the models, but since I didn't have access to a MATLAB instance I decided to reproduce the same set of diagrams using Perl. After a couple of weeks of experiments and several emails to the author I was able to model various types of neurons according to the parameters described in Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting [?]. Here is how the results look for the regular spiking (RS) neuron:
And here are the results for the chattering (CH) neuron:
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