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Let'a study a famous neural network model, the Wilson-Cowan
equations. Here is the ODE file:
# wilson cowan
It is a two-dimensional system. Run XPP and get yourself on a solid
fixed point by tapping i g and then i l a few times. Now
run AUTO. The parameter we want to vary is c. Set up the Axes so
that the Y range is 0-1.1 and the X-range 0-10. In the Numerics menu
set Par Max to 10 and Dsmax to 0.2.
Run from a steady state. Find the Hopf point and
then find the periodic orbit. Explain the diagram. How is the periodi
orbit born? Is it super- or sub-critical? How does it die? What
happens for very large inputs, c? Is this system bistable?
G. Bard Ermentrout