Dynamical systems and system dynamics models

[Martin Schaffernicht]

Hello everybody,

the following is a purely academical question.

I am wondering about the relationship between "dynamical systems" and "system dynamics models". The latter describe "feedback-driven" systems. If the "dynamical" essence of a system is generated inside the system (otherwise, would it be a system at all?), then I'm tempted to think that any "dynamical system" can be described as a "feedback-driven" system and thus represented by a "system dynamics model".

(I know this may be little practical sometimes, but my question is "in principle".)

Am I wrong? If so, then: why?

Best greetings,
Martin Schaffernicht
U. de Talca (Chile)

[Jim Duggan]

Hi Martin,

Interesting question... I have been reading (and struggling with!) a really good book on dynamical systems recently "Non-linear dynamics and chaos" by Steven H. Strogatz. THis focuses on the mathematics of dynamical systems, including first order differential equations, phase plane analysis,bifurcations, chaos, Lorenz equations, etc.

The approach seems mostly focused on using calculus to help solve engineering problems, whereas SD uses calculus to explore feedbacks of social systems.The mathematics of dynamical systems can be applied to SD models also. For example, Strogatz has interesting linear 2nd order models, and provides analytical solutions to these using eigenvalues, and in SD, this approach is the basis of formal loop analysis.

There are a good number of SD papers that focus on chaos (I think there was a special issue of the SDR in 1988), and in the 50-year special issue in 1997, Erik Mosekilde had a paper on non-linear analysis of the beer game.

So I would say both approaches have a lot in common, but it is the specific focus on feedback, social systems, and policy that is unique to SD.


regards,
Jim.

[Martin Schaffernicht]

Thanks Jim!

Why is the focus on "feedback loops" limited to so few groups of people? I know there are differences between cybernetics and SD, but apart these two communities, loops do not seem to be very important.

Since they do have importance for SD, I have a dissonance here.

From an ontological point of view, I interpret texts like "principles of systems" as saying that the (revelant) social (dynamical) systems are made of interacting feedback loops. Even if one wishes not to say that such loops are "really there", at least there is the firm message that feedback loops are an always useful (valid) way to think about social (dynamic) systems.

From a cognitive point of view, I believe loops allow to "chunk together" many details, a little like the exemplary chess expert who recalls the entire configuration as one (where the novice has to store and recall each single piece). So there is a certain economy in using loops thinking.

However, if you are strong in mathematics, and you treat problems that can be solved analytically, maybe loops do not have so much value added? This would mean there are other ways to think about dynamical systems that are as useful (valid) as feedback loops. But then I wonder how such "ways to think" relate to each other. Can any analytically represented dynamica system be translated int a SD model? And the other way around?

Hmm, then when I think of my MBA students (who were not trained mathematicians), once they had got the idea, they loved loops and started detecting them everywhere...
... when the everiday decision maker reasons about a problematic situation, will there be feedback loops on his mind? Can he be rather unaware of them as structure but more aware as behaviors or chains of events? Experimental evidence suggests that usually there is little awareness of loops and (for instance) exposure to simulators does not augment this awareness. Still, the sudden recognition that the world around us is a complex of interacting feedback loops is a real "conceptual change": once you've gone through it, you don't get back.

This is quite a riddle to me. I guess that early exposure to feedback-thinking would not fail to help. Also, I'm aware that system dynamics is more than just loops, but I find loops easier to explain than delays or stock-flow relationships. And I need to expain this quite frequently: each time fellow economists or other colleagues come to a presentatio of SD-work, some of them later ask me "why don't you simply use the same tools as everyone else? What's the advantage? (What would make the effort of learning a new language worth the pain?)"

Well, your answer has helped me reflect upon this, so thanks!

Martin

[Jean-Jacques Lauble]

Hi Martin

I am not loop thinking like you. And there are reasons for that.

I have a model with 7000 loops each loop having an average of two subscripts. It makes approximately 100000 loops to study! What is the interest of being loop thinking in this case?

Another reason: I have presently finished the first step of a model that is very simple at this stage.
I have built a continuous model and a discrete model, representing exactly the same problem, but differently, using the same language Vensim and that give roughly the same results. The discrete model has one loop and is much closer to the reality than the continuous one. This only loop is very short and represents a simple capacity constraint. The continuous model has 6 loops. A previous model had 14 loops but had a week time step that necessitated more material to take into account the longer time step. Now the continuous model has a day time step. I prefer the day time step for some reasons that have nothing to deal with the loops. It seems to me that the loops represent the way you describe the reality but do not necessarily characterize it.

About decision makers being loop thinkers, All of them do not even know what a feedback loop is. And when I take day to day decisions I never think about feedback loops. But the decision makers I know, are certainly stock thinkers, whether explicitly or implicitly and I am too all the time. You think about your cash which is a stock, the delay of your clients payments which is a level, about any situation (financial etc…) which is always a level. Levels are there all the time. Feedback loops very seldom, or eventually as virtuous or vicious circles, or sayings as 'trees do not grow for ever'. But they will not think about their nature and how they are related to the levels.

I make two separate models discrete and continuous because it helps me to have two different points of view and avoid the trap of being stuck with a unique representation of reality. It gives you a fell of the relativity of any representation. One model helps me too to debug the other. The continuous one is structurally more difficult to understand, but has the big advantage to run 10000 times quicker that the discrete one. The discrete one, already at this stage is nearly impossible to use with Synthesim. Of course I will study the 6 loops of the continuous model, because I may learn something from them, but it does not make me systematically a loop thinker.

Another remark. All loops either from the continuous or discrete models flow through the same level that represent the same thing in the reality. I think that what characterizes reality are the levels and not the feedbacks. This is why decision makers think mainly about levels.

Regards.
Jean-Jacques Laublé.

[Jim Duggan]

Hi,

An interesting quote I came across that relates to SD and feedback loop thinking, and the generality & validity of SD as a theory.

"Various critics have asked that the generality of feedback loop structure be proved. Such a request fails to recognize that this class of theory is not subject to positive proof. Once the theory has been stated and a range of acceptable examples are given, the only possible proof is negative. If one can show an important and purposeful decision which is not embedded in a feedback loop structure then the generality is destroyed."

Jay W. Forrester. "Industrial Dynamics - A Response to Ansoff and Slevin". Management Science. Vol. 14. No. 9. May 1968.

regards,
Jim.

[Martin Schaffernicht]

Thanks to both of you!

I see there are different possible opinions and I do not have the expertise to advance an authotitative opinion myself.

It has also happened to me that the number of feedback loops (even in relatively small models) is threatingly high. I've also taken notice that the number of apparent feedback loops changes according to how many or few auxiliary variables one uses toformulate the problem. So if there is a simpler way to deal with it and that fulfills the purpose

Concerning the idea that stocks are more real than loops, I agree that loops seem to be an emergent entity with respect to stocks, and stocks are more salient. I've wondered many times why the way to talk about a loop's behavior is to talk about the behavior of one of its variables.

Still I feel that I don't agree that loops are not real.

I started this question because I'm interested in "mental models of dynamic systems" and with a friend, we believe that if dynamical systems are driven by feedback loops, then mental models of them ought to consider loops, too. Reading your posts, I've found a new question: would (other things being equal or controlled for) one individual who thinks about a problem in terms of feedback loops do better in a dynamic problem than another individual who thinks in terms of stocks?

Thanks,
Martin

[Magne Myrtveit]

I've also taken notice that the number of apparent feedback loops changes according to how many or few auxiliary variables one uses to formulate the problem.

The word "apparent" is important in your sentence, Martin. Feedback has to do with stocks and flows only. To see the real dynamic links in a model, you should remove all auxiliaries and have just one flow per stock. (Put auxiliary equations into the flow equations, and merge multiple flows of a stock into one).

When this is done, you have feedback through a stock if and only if there is a direct or indirect dependency path from the stock back to its own (net) flow.

Adding auxiliaries does not create more loops; it just creates more detail to the paths from stocks to flows. (Paths that do not start from a stock and end at a flow can be removed completely when you study feedback).

Even with the above simplifications, the number of feedback loops gets overwhelmingly large even for relatively small models. The art of finding the dominant loops is therefore a key to making any sense out of the loops. I write "art", because I am not aware of any robust scientific solutions, technical implementations, and graphical visualization for to solving this problem among the current simulation tools. (There are some "toy" solutions around, but much research and development is still to be done in this area).

Best regards,
Magne Myrtveit
http://www.dynaplan.com

[Jean-Jacques Lauble]

Hi Jim, Magne and Martin
I have never written that feedback loops were not real. I wrote that some feedback loops were relative to the way the model is built. There are certainly loops that are relative to the problem and some relative to the model itself like Magne suggested.
I wanted to discuss about the practical utility of thinking about loops and still think that it may be sometimes very useful and sometimes misleading, depending on the subject, the time resources one has to study the model, the experience of the modeler and the client, the existence or not of implementable policies to cure the effects of some harmful loops. I think that being too much loop thinking is overselling SD. And overselling the method is deadly. When I think about the big mistakes I have made in my life, none were generated by not considering some feedback effects, but by being too optimistic and not considering that only things that cannot happen, never happen. It is then necessary first to list events that can happen, which is not evident, and then imagining scenarios that make them happen and then organizing ways to lessen their effects if they happen.
To resume be prepared for the worst imaginable.
I think that the prime reason of poor adoption of SD, is that most people do not take the time to think about problems even with simple methods. If they did it, they would soon recognize in some cases the need to use more adapted methods like SD. Before rushing to SD, I prefer to analyze the problem in a linear or static fashion and make sure that I have fully understood the problem this way.
Is Martin absolutely sure that his students are able to fully analyze a problem with a static or so called linear way of thinking? It helps to start with a static point of view when it seems necessary to use a more sophisticated method later on.
I think this way because I am not selling SD, and am concerned by solving the problem. I am then problem oriented and not anything else oriented.
When I develop a model, I always try to evaluate the gain that was generated by going a step forward into more sophistication.
Regards.
Jean-Jacques Laublé

[Martin Schaffernicht]

Hello Jean-Jacques and Magne,

first my apologies to Jean-Jacques, I wrongly interpreted the sentence "I think that what characterizes reality are the levels and not the feedbacks" in the sense that you think stocks are more real than loops.
I am not sure that my students "are able to fully analyze a problem with a static or so called linear way of thinking". What I occasionally do is ask them to map (factual or possible) events rearly on. Then we identify the variables that are implied be the events. However, in my course I've seldomly seen a student work through a problem with a model without loops; however, this may be my own fault, because I select the problems they work and I orient them.
The other thing I started to do is make them start the conceptualization phase with stock-and-flow diagrams rather than CLDs and leave the CLDs drawing until the end, when behaviors have already been simulated and analyzed.
I started that because I wanted students to be more precise in their thinking (and my impression is that CLDs are not so good for this, but that may be attributed to my own faults). But with Magne's message in mind, my impression is that be setting out with CLDs that do not even distinguish between stocks and other variable types, may also be little desirable for the reason that one would tend to overdo the search for possible loops.
So it seems that the recommendation to articulate the logic of policies using auxiliaries (such as to visualize the logic) has a price in form of being overzhelmed by detail-aspects of feedback loops. So should students be advised to develop such a "collapsed" version of the model (with only one net flow rate and all auxiliaries hidden inside)?
As one of these people who try to learn SD on their own (using books, communication with others and trial-and-error), I must say this does not become clear by reading any of the SD textbooks. Maybe this has to do with that it is still an "art" and as such it is hard to write about? Even so, at least the idea that not all loops implied by the causal structure may be important and that loop-dominance will usually change over time could be incorporated in texts directed to students of SD.
Well, another aspect of this discussion is that maybe in "mental models" studies, we ought to pay attention to if the subjects recognize some variables as "stocks" (not by their name but be their characteristic).
To end, I wonder how "mental models" of SD-practitioners and "other people" would compare if we put them in two separate groups, brief them in an initially unknown situation and make them solve a dynamic decision task in a simulation game. Would one of the groups outperform the other? Would the "winners'" group's mental models be more complex, have more recognized feedback loops? I am not aware that this has been done already, so that is one thing I'll try to find out.
Thanks to you all (and sorry for the misunderstanding),
Martin

[Thomas Fiddaman]

There's a nice survey of methods for structural analysis here http://www.systemdynamics.org/conferences/2007/proceed/papers/OLIVA434.pdf