Vensim works according to a mathematic equations? Anyone can help me, please?!

[sya282]

I developed a model mathematically and tested the model to find an equilibrium point on a Vensim software. Briefly, I developed a model to see how people change their opinions about climate change risk. Green opinion group, Neutral group, Grey group. I want to see equilibrium status for these groups corresponding to parameter changes.

Mathematically, I found equilibrium points corresponding to parameter changes. When I run the program, it works in some cases, matching with the mathematical equation, but in other cases it doesn't match with the mathematical results. The value just goes to extreme, either to the maximum value and zero.

For example, when I set the population of these opinion groups = 1000. When I set two parameters= 0.11 for both, they reach an equilibrium point for three groups (346 for green, 346 for grey, 307 for neutral). However, When I change one parameter 0.11 and the other 0.12, grey group goes to 1000 and green goes to zero.

The equations for the equilibrium point of the green opinion group is

The rate of change of a green opinion group is
= 𝝓si * Nn * 𝝆 * 𝜷* Ngn/P – 𝝓si * (1 - 𝝅agn) * (1-𝝅ign)* 𝝆 * 𝜷* (1- 𝝅agn)* Ngn* Ngy/P

At steady state dNgn/dt must equal 0
That means
Nn = Ngy * (1 - 𝝅agn)2* (1-𝝅ign)
Ngy = Nn / (1 - 𝝅agn)2* (1-𝝅ign)

[Administrator]

Can you upload the model? It's very difficult to suggest anything without seeing the model.

[sya282]

Social contact.mdl

This is the model I developed

(4.54 KiB) Downloaded 475 times

In the model, I want to see equilibrium status while changing the rates of Green ideo (green ideology), Green affec (Grey affective), Grey ideo (Grey ideology), and Grey affec (Grey affecitive).

In math equation, whatever I put the value, there are always equilibrium points. If I put Green ideo = Grey ideo = 0.11 and Green affec = Grey affec =0, the Stella model reaches equilibrium (Green=Grey=346, Neutral=307) as same as the equation. However, if I put Green ideo = 0.1, Grey ideo = 0.11 and Green affec = Grey affec =0, the equation shows the equilibrium like Netural 309, Green 347, and Grey 343. but the Stella model goes to extreme.....Could you please help me to figure out this issue?

Thank you very much!!!

[tomfid]

There are some unit errors here that could indicate the problem. The first is that "unitless" is not a known synonym for "dimensionless" (which Vensim understands). You can add an entry to Model>Settings>Units, like

dmnl,dimensionless,unitless

After that, there are still some issues related to "percent".

I think there may also be equation errors. For example:

(1-Green affect)*Stickiness*(1-Green ideo)*Mixing rate*(1-Green affect)*Green*Grey/Population

The appearance of (1-green affect) twice seems odd, though I'm not clear on the intent here.

[sya282]

Thank you for informing me those errors! Since I am a beginner of the Vensim, I should be more familiar with the system. I will correct them!

Concerning the (1-green affect), I intentionally add (1-green affect) twice to correspond to a theory I apply for this model.

This odd behavior was probably occurring because there was more than one stable state, or an unstable equilibrium in my input.

Can Vensim determine the stability of equilibrium points of the equation I entered? or Do you have any suggestions?

[sya282]

Thank you for informing me those errors! Since I am a beginner of the Vensim, I should be more familiar with the system. I will correct them!

Concerning the (1-green affect), I intentionally add (1-green affect) twice to correspond to a theory I apply for this model.

I suspect that this odd behavior was probably occurring because there was more than one stable state, or an unstable equilibrium in my input.

Can Vensim determine the stability of equilibrium points of the equation I entered (evaluate whether equilibria are stable or unstable)? or Do you have any suggestions?

[tomfid]

There isn't really an easy, general way to do this, but you could do something like the following.

You have 3 stocks, but since they're conserved, there are really only 2 degrees of freedom. So you could parameterize the initial values of the stocks as something like:

neutral = population * frac neutral
green = population * (1-frac neutral) * frac green
gray = population - green - neutral

Then it would be easy to explore the (frac green, frac neutral) space in Synthesim to see how the terminal equilibria vary (if they do).

[sya282]

I tried a new design...and it didn't work out ....T.T....