## Gumowski-Mira-Attractor

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josef
Junior Member
Posts: 2
Joined: Mon Aug 29, 2011 12:29 pm

### Gumowski-Mira-Attractor

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 Gumowski-Mira-attractor 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(1-b*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

Josef Boehm
Posts: 4466
Joined: Wed Mar 05, 2003 3:10 am

### Re: Gumowski-Mira-Attractor

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.
http://www.ventanasystems.co.uk/forum/v ... f=2&t=4391

Units are important!
http://www.bbc.co.uk/news/magazine-27509559
tomfid
Posts: 3774
Joined: Wed May 24, 2006 4:54 am

### Re: Gumowski-Mira-Attractor

Here's an example, which also shows in general how to handle discrete time math.
gumowski mira.mdl
The behavior is really amazing.

Tom
josef
Junior Member
Posts: 2
Joined: Mon Aug 29, 2011 12:29 pm

### Re: Gumowski-Mira-Attractor

Hi Tom,

many thanks. This helps a lot.
You are right the graphs are very amazing.

Regards
Josef
gwr
Senior Member
Posts: 209
Joined: Sun Oct 04, 2009 8:40 pm
Vensim version: DSS

### Re: Gumowski-Mira-Attractor

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 Gumowski-Mira-System a bit of algebra will convince you that no delays are needed.

See the model enclosed.

Cheers,

Guido
Attachments
gumowski mira.mdl