Re: LOGO-L> Volterra-Lotka model

[George Mills <mills@softronix.com>]

MHELHEFNY@FRCU.EUN.EG wrote:
> 
> Erich Neuwirth wrote :-
> 
> 
> i think one should discuss a little bit more
> why these equations make sense,
> and we also should talk about george's remark
> that it is not so easy to find "working" values
> for the parameters.
> 

Your using my remark in the wrong context.

We are talking about 2 completely different methods in solving
preditor-prey problems. The methods that Erich and Mhelhefny
are discussing are completely different approaches from what
I proposed. There is no differential equations involved with
my method (7th grade math is all that is needed).

The method I proposed can also handle much more complex
models which would even cause the most advanced mathematician
to pull his/her hair out.

As I had spoke about before you can include rules such as.

Wolves travel in packs.
Baby bunnies tend move with their parents.

Here is a crude example:

4x4 cells each cell containing [Rabbits Wolves]

Iteration 1 (initial conditions):

[0 2] [0 0] [0 0] [0 0]
[0 0] [2 0] [0 0] [2 0]
[0 0] [0 0] [0 1] [0 0]
[0 0] [0 2] [0 0] [0 0]

Iteration 2a (reproduction/consumption):

[0 3] [0 0] [0 0] [0 0]
[0 0] [8 0] [0 0] [2 0]
[0 0] [0 0] [0 1] [0 0]
[0 0] [0 2] [0 0] [0 0]

Notice some cells had reproduction that had multiple
animals of the same type (sometimes).

Iteration 2b (traveling):

[0 0] [2 1] [0 0] [1 0]
[2 1] [2 1] [0 0] [0 0]
[0 0] [2 0] [0 1] [1 0]
[0 0] [0 1] [0 1] [0 0]

There are still the same totals but they have randomly
moved around.

Iteration 3a (reproduction/consumption):

[0 0] [1 1] [0 0] [1 0]
[1 1] [1 1] [0 0] [0 0]
[0 0] [2 0] [0 1] [1 0]
[0 0] [0 1] [0 1] [0 0]

Notice 3 bunnies became dinner for 3 wolves
and no reproduction this time.

Iteration 3b (traveling):

[0 0] [1 1] [1 0] [0 0]
[1 1] [1 1] [0 0] [0 0]
[0 0] [1 0] [0 1] [0 0]
[0 0] [1 1] [0 1] [1 0]

And so on.

For each cell

Consumption formula:

If :Wolves > :Bunnies [Make "Bunnies :Bunnies - :Wolves] ; Each wolf ate
1 bunny
If 0 > :Bunnies [Make "Bunnies 0] ; Can't have negative population

Reproduction formula:

If :Bunnies > 2 [Make "Bunnies :Bunnies + 6]
If :Wolves > 2 [Make "Wolves :Wolves + 1]

An Example of choosing a "parameter" I mentioned
is choosing how large a liter is (6 and 1 above).
What I did here is very crude since I did not track
age or sex (but I could of).

Traveling:

This is tricky and let you discover the types of problems
you can run into.

Again, this is extremely crude version but is actually
usable. You can make the formulas as complex as you
like and the information contained in the cell as
rich as you need. You could even put Hiding places
in the grid that the Bunnies can hide in from the wolves,
but there might not be any food in those places for
the bunnies.

You could do some cool stuff with graphics and watch
things happen.

You could spend a couple hours to a couple years on this
problem.

-- 
===============================================================
George Mills
email: mills@softronix.com
http://www.softronix.com
The www page contains some very powerful educational software.
Our single most important investment is our kids.
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