Instructions for investigating a simple neural network model with
delays.

Download nn1delay.ode from the course website and run it in XPP.

1. The parameters should be set by default to tau = 0, w=1 and theta=0.
What do you expect the steady state to be in this case?  Use [I]nitial
conditions, [R]ange to see trajectories from multiple initial
conditions.

2. Keeping tau=0 for now, explore the (theta, w) parameter regime (theta
is called "th" for convenience).  Find a point at which the system shows
multistability.  Illustrate multistability using

3. Set the parameters so the system is at the cusp of the multistable
region.  What do the trajectories look like now?

4. Set the parameters to w=6, th=3.  Introduce a delay by setting the
parameter tau to 1.  Try different initial conditions to look at the
effect of the delayed feedback. Explore different delays, different
thresholds and different levels of feedback. What difference do you
observe between positive and negative delayed feedback? For negative
feedback, make the weight w negative.  If nothing "interesting" happens,
try a longer delay.  Change n[U]merics [T]otal to a larger value (say
200) and change [V]iewaxes [2D] x limits to see longer runs.  Use
[W]indow [F]it to zoom into the correct scale automatically.