Subject: managing innovation using stock and flow diagram

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

Message:

The recent disagreements here about chaotic systems can be reconciled by noting that Paul's comments refer to continuous models while Dexter's original statement referred to discrete models.

It's easy to get non-repeating dynamic behavior out of a single equation (single stock?) if the equation is discrete, e.g., the famous quadratic

X(t+1) = 1 - a * X(t)^2

[If you haven't played with this, do this in a spreadsheet: Let a = 1, start with X(0) = .2, say, and see the sequence of X's (simple oscillation). Then let a = 2 and see the new (longer) sequence (messier). Let a = 3, etc. As the parameter a gets bigger the system becomes chaotic (somewhere after a = 3, I think).]

But Paul is right that in continuous systems, which are the sort that system dynamicists are presumably working with, at least three stocks are necessary to produce non-repeating oscillations and the inordinate sensitivity to initial conditions that characterizes them. The simple classic is the Lorenz model (the structure diagramed on the opening page my web site).

But the bigger questions here ought to have more to do with helping the original person (Ah Kau Lim) posting a question abut managing innovation. That question isn't about chaos or, at this early stage, not even about equations, or even about stocks and flows. We need some help thinking about how to define the problem and begin thinking about it.

I'd say Lim ought to start by thinking about the dynamics of interest and representing them in graphs over time. Ideally, then, Lim would appeal to existing theory about the dynamics of innovations and start to think about how to represent that in feedback terms. After all, just because we have system dynamics tools at our disposal doesn't necessarily mean we are smarter than everybody else who's thought about the dynamics of innovations. Once we have some idea of how we might diagram with previous scholars have thought, and maybe tested those ideas with simulation, then we could be gin to think about how we might make a distinctively "system dynamics" contribution.

Follow Ups:

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