Equations:
$$\partial V / \partial t = \frac{1}{\epsilon}(V - V^3 / 3 - W)$$$$ \partial W / \partial t = \epsilon (V - \gamma W + \beta)$$Plotting the nullclines (curves along which the time derivative of V and W are zero). By setting the derivatives above to zero, we can combine both to form the following equations: $$V - V^3 = W$$ $$1 / \gamma V + \beta = W$$
This combines into the following parametric curve W as a function of V: $$ V - V^3 - 1 / \gamma V - \beta = 0$$
def PlotNullclines(gamma, beta):
"""Plot the V- and W-nullclines for specified gamma and beta.
Optionally also find the fixed point (vstar, wstar) for the
specified gamma and beta, and plot the (vstar, wstar) as a point
along with the nullclines.
Using pylab, multiple calls to pylab.plot() can be used to
plot the various curves in one figure. To plot only the
nullclines, you may want to include a call to pylab.show() in
this function, but you may want to remove it later when plotting
nullclines along with trajectories.
"""
pass