1. Consider a model for the activity of a neuron dy dt =g+tanh(c) a) Use MATLAB to simulate the dynamics when c = 1/2. Start the dynamics at y = 0.5, and plot the solution y(t) against t for t = 0 to 5. In a separate figure, produce a plot of the functions f(x) = x, and g(x) = tanh (cx). How many equilibria are there when c = 1/2? b) Use MATLAB to simulate the dynamics when c = 2. Start the dynamics at y = 0.5, and plot the solution y(t) against t for t = 0 to 5. In a separate simulation, start the dynamics at y = -0.5, and plot the solution y(t) against t for t = 0 to 5. In a third figure, produce a plot of the functions f(x) = r, and g(x) = tanh(cx). How many equilibria are there when c = 2? c) Is there a bifurcation as c increases from 0.5 to 2. What type of bifurcation? If there is a bifurcation, for what value of c does it occur?