I like Vensim PLE and I am preparing a paper for a teachers’ inservice course using PLE and other tools.
I wonder if it is possible to model the GumowskiMiraattractor given by the following system:
There is a function g(x) defined (specially g(x)=0.9x 2*(1+0.9)*x^2/(1+x^2)
Then
xn = yo + a(1b*yo^2)*yo + g(xo)
yn = xo + g(xn)
x0 = y0 = 0.1 (initial values)
xn = x new; xo = x old
yn = y new; yo = y old
Many thanks in advance
Josef Boehm
GumowskiMiraAttractor

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 Posts: 3041
 Joined: Wed Mar 05, 2003 3:10 am
Re: GumowskiMiraAttractor
I don't see why you cannot do it. To get the old values of x, y and G, use DELAY FIXED with a delay time of one time step.
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http://www.ventanasystems.co.uk/forum/v ... f=2&t=4391
Units are important!
http://www.bbc.co.uk/news/magazine27509559
Re: GumowskiMiraAttractor
Here's an example, which also shows in general how to handle discrete time math.
The behavior is really amazing.
Tom
The behavior is really amazing.
Tom
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Re: GumowskiMiraAttractor
Hi Tom,
many thanks. This helps a lot.
You are right the graphs are very amazing.
Thanks also for the link,
Regards
Josef
many thanks. This helps a lot.
You are right the graphs are very amazing.
Thanks also for the link,
Regards
Josef
Re: GumowskiMiraAttractor
Hi Tom,
I do not see any reason for using a DELAY FIXED here. You can handle discrete systems  e.g. difference equations' systems  using the regular System Dynamics notation. What you need to do is:
1. Set the time step to 1.
2. Convert the Stock Equations into difference equations, e.g. Delta X = X(t+1)  X(t) = dx/dt with dt = 1.
3. In the case of the GumowskiMiraSystem a bit of algebra will convince you that no delays are needed.
See the model enclosed.
Cheers,
Guido
I do not see any reason for using a DELAY FIXED here. You can handle discrete systems  e.g. difference equations' systems  using the regular System Dynamics notation. What you need to do is:
1. Set the time step to 1.
2. Convert the Stock Equations into difference equations, e.g. Delta X = X(t+1)  X(t) = dx/dt with dt = 1.
3. In the case of the GumowskiMiraSystem a bit of algebra will convince you that no delays are needed.
See the model enclosed.
Cheers,
Guido
 Attachments

 gumowski mira.mdl
 (5.84 KiB) Downloaded 164 times
Re: GumowskiMiraAttractor
Guido,
You're entirely correct. The INTEG notation that you used is probably the nicest way to do this for formal correspondence with discrete derivative notation. However, as long as TIME STEP=1 and Euler or Diff integration is used, the results will be identical whether INTEG, SMOOTH, or DELAY FIXED is used. (Diff integration is the same as Euler, but the rates and levels are stored differently, which makes it easier to see the initial values of the rates  sometimes useful for discrete systems like this.)
Tom
You're entirely correct. The INTEG notation that you used is probably the nicest way to do this for formal correspondence with discrete derivative notation. However, as long as TIME STEP=1 and Euler or Diff integration is used, the results will be identical whether INTEG, SMOOTH, or DELAY FIXED is used. (Diff integration is the same as Euler, but the rates and levels are stored differently, which makes it easier to see the initial values of the rates  sometimes useful for discrete systems like this.)
Tom
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