Sunday, May 24, 2009

More parameter space of "standing" circuit

Using the parameter space maps made last time, I've set the "standing" circuit into a place where it has a nearly symmetric bi-stable steady-state at p1 =0.25 and p2=0.50.

The following is the derivative at a given concentration of standing. This dy/dt vs y plot (I don't know if there is a correct name for this find of plot) shows that there are two stable steady states at the zero crossings -5, and +5. There's also the unstable point near zero. It is not exactly at zero because the gate model functions do not cross at zero as seen below.

Now I continue the analysis with the "tired" half of the circuit. I'm interested in the response of "tired" when the "standing" input reaches 0, the point at which the tired circuit will charge fully.

Charging of the tired circuit when standing is 0 and tired starts at its steady-state value of -5

So, "tired" reaches 0 (the point at which the gate 5 is going to be fully on) within about 20 time units when standing = 0.

The following is a sampling of the parameter space for p1 and p2 given "standing" = 0. The steady-state value of tired changes as a function of p1, so for each graph I've started "tired" off at the appropriate steady-state and then watch the evolution when "standing" = 0. This demonstrates that I can delay both the onset of tired (when it hits zero) and how high tired gets at steady-state by adjusting these two parameters.

Next up, I put the circuit back together again...

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