You can find parameter values and equations for all models in this assignment 
<a href="http://www.math.pitt.edu/~bard/bardware/neurobook/allodes.html"> here</a>
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<b>Problem 1</b> (For those who have not played with Morris-Lecar model before)
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In the Morris-Lecar model generate the fI curve for parameter values both in Type I and Type II dynamic regime.
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<b>Problem 2.</b>

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Use a model with T-type calcium current and spikes blocked (!!!). it is a 2-variable model so phase-plane analysis can be used. This a depolarazing calcium current that has both activation and inactivation, and activates at low voltages (note the location of the gating variables' infinity curves). (It also has a slightly unusual driving force)
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a) Set the leak reversal potential at -60 mV. What will the model do with no input current? What are the values for the T-current and its gating variables? Why? How will the cell respond to brief pulses of depolarization and hyperpolarization? You should see that it is activated by hyperpolarization, not depolarization. Explain why hyperpolarization has this effect using nullclines (what happens to the nullclines during hyperpolarization? what does solution do? what happens to the nullclines when the hyperpolarization is gone and where does the solution go?) and why depolarization does not work.
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b) Now a neuromodulator is added that brings the leak reversal (rest voltage) down to -80 mV. What effect does depolarization pulse has now? Why?
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c) speculate what effect the neuromodulator from b) (or its absence) would have in a network of cells with T-current.
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<b>Problem 3.</b> (for those who did not have to do problem 1 and/or have played with T-current before).
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Use Desteche-Pare model with M-current from the link above.
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a) With M-current turned off: Vary I applied from -6 to 6 and observe number of steady states and/or oscillations in the model. Summarize steady states in a diagram, similar to a bifurcation diagram. Do you think this model has type 1 or type 2 dynamics?
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b) now make g_m=2 mS/cm^2. What effect does M-current have on the spike train with constant applied current I=6? Now repeat a) with this M-current model for I from 0 to 6. What type of dynamics is this now?
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This is another model that can switch from type 1 to type 2 by varying a single parameter. M-current can also switch a neuron to (what is sometimes called) type 3 excitability - when the neuron responds only to transient but not to ongoing stimuli
(e.g. Prescott SA, Ratté S, De Koninck Y, Sejnowski TJ.
Nonlinear interaction between shunting and adaptation controls a switch between integration and coincidence detection in pyramidal neurons.
J. Neurosci. 2006; 26: 9084-9097. )