It occurs to me that one thing you could do for knowing what the parameters should be, and how to interpolate with the right finite sampling frequency is to do dimensional analysis like is done with non-linear equations in fluid mechanics.

for ex. If we have the modified van Der Pol equation, by introducing another parameter:

x''(t) + e (x(t)^2 -1) * x'(t) + w^2 * x(t) = s(t)

where s(t) is the signal input and x(t) is the system's output:

we could consider x as having units of Volts, w as having units of rad/sec, and e as having units of 1/sec*V^2. Then, we could form dimensionless groups of variables that make this equation dimensionless. fs is the sampling frequency of simulation (the interpolated sampling freq) and a new variable y could be added that normalizes the signal amplitude, y= 1 V

we could rewrite this equation as:

x''(t) * 1/y*fs^2 + ((x(t)^2 -1) * x'(t) *e/y*fs^2 + x(t)* w^2/y*fs^2=s(t)/y*fs^2

Then, we could have two notable dimensionless groups: pi1=e*y^2/fs^2 and pi2=w^2/fs^2

For two different systems, we can expect the same behavior, if pi1 and pi2 are the same for the different systems. You would still have to determine values of pi1 and pi2 over which different types of system behavior occur, and that can be an arduous process. Maybe someone has already done this?

That's just an example of how this dimensional analysis idea might work. I don't rightly know what types of systems you all are looking at.

-- Charles Zachary Henry

anti.dazed.med Med student who needs a Mickey's