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Analog vs digital X-Y mode
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nctnico:
Are there any loss-less wav files available for the clock so people can try without needing the actual hardware?
CopperCone:
for constallation diagrams
rstofer:
Over in a distant corner of the electronics sandbox, a few of us play with analog computing.  Not many people over here...

X-Y mode is critical.  We usually use one integrator to provide the X axis and the output drives the Y axis.  There are cross-coupled differential equations that draw a kind of egg-shaped pattern.  Not a circle, more like one that has been stomped on.  It's interesting to print two channels of Y(t) but more interesting to plot the simultaneous values of X and Y.

FWIW, the classic example is the Predator Prey problem.  As the rabbit population increases, eventually there will be more foxes.  More foxes will drive down the rabbit population which will reduce the fox population allowing the rabbit population to increase, and so on.

When I want X-Y done well, I use my Analog Discovery 2.  Among other things, I get a better screen shot.
mtdoc:

--- Quote from: rstofer on April 29, 2018, 01:42:15 am ---FWIW, the classic example is the Predator Prey problem.  As the rabbit population increases, eventually there will be more foxes.  More foxes will drive down the rabbit population which will reduce the fox population allowing the rabbit population to increase, and so on.

--- End quote ---

Lotka–Volterra equations
rstofer:

--- Quote from: mtdoc on April 29, 2018, 03:25:58 am ---
--- Quote from: rstofer on April 29, 2018, 01:42:15 am ---FWIW, the classic example is the Predator Prey problem.  As the rabbit population increases, eventually there will be more foxes.  More foxes will drive down the rabbit population which will reduce the fox population allowing the rabbit population to increase, and so on.

--- End quote ---

Lotka–Volterra equations

--- End quote ---

Exactly!  I need to read through that document.  About half way down they give the X-Y plot that I was discussing above.  Both populations are displayed on a single graph.

These equations don't have to be put into an actual analog computer.  MATLAB does a fantastic job of modeling the required integrators (2) and gain stages.  Simulink  gives the same answers without all the op amps.  But I like the old-school approach.  There's just a warm fuzzy feeling as the integrators integrate, the multiplier multiplies and the gain stages do their thing.

Attached is the Simulink model

Note that the model is pretty superficial.  As the article points out, the assumptions are probably not realizable.  Notably that the Prey can grow without bound because there is always adequate food.  The model could be improved to account for an exponential growth asymptotic as some logistic limit.

In my view, the X-Y mode more appropriately displays the interaction between the populations.  The Y(t) mode is useful but the X-Y mode drives the point home.

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