Subject: managing innovation using stock and flow diagram

Posted by Paul Newton on 1/30/2009
In Reply To:managing innovation using stock and flow diagram Posted by Dexter Chapin on 1/29/2009

Message:

Hi Dexter! I want to question one statement you made, "It is possible to build a chaotic system with only one flow in and one flow out of a single stock." My understanding is that a chaotic system is at least roughly defined as one which produces oscillatory behavior in which the periods and amplitudes of the oscillations don't repeat themselves in any discernably regular manner, and that the simplest system that can produce chaotic behavior must contain at least three stocks. I further understand that the Lorenz Attractor model is an example of such a minimal chaotic system, as it contains only three stocks. Tom Fiddaman created a version of this model and has posted it for download from his model library - see http://www.metasd.com/models/index.html#Science.

I always think of it this way.. In the same way that two stocks are required to produce oscillatory behavior, three stocks are required to produce chaotic behavior. So, it is impossible to get chaotic behavior from a one stock model.

However, if one does see what appears to be chaotic behavior from a one-stock model, my guess is that the behavior is really caused by delays in the model being too short relative to the time step of the model, producing what Andy Ford in his "Modeling the Environment" book calls "artifactual behavior," that is, the model's behavior is an artifact of the calculations in the model, and not representative of what is going on in the real world. I think such artifactual behavior can be chaotic. I recall playing with such a model a few years ago that had actually been published in textbooks and peer-reviewed academic journals, and I think the model I was playing with purported to replicate observed chaotic behavior in the lifecycle of lake fly populations. I think, however, that although the model behaved in accordance with observed real-world behavior, it was doing so for artifactual reasons that had very little to do with the real world reasons for the observed chaotic behavior.

Just my two cents worth on this, and not really on the topic of innovation, but rather on modeling practice.

Paul Newton

Follow Ups:

managing innovation using stock and flow diagram - George Richardson 1/30/2009 
managing innovation using stock and flow diagram - Lees N. Stuntz 2/2/2009
managing innovation using stock and flow diagram - Jeffrey S. Levin 2/1/2009
managing innovation using stock and flow diagram - Niall Palfreyman 1/30/2009
managing innovation using stock and flow diagram - Dexter Chapin 1/30/2009