Can chaotic systems be predicted? I guess we first need to agree on exactly what a chaotic system is.
BusinessDictionary.com defines it as a
“Complex system that shows sensitivity to initial conditions, such as an economy, a stockmarket, or weather. In such systems any uncertainty (no matter how small) in the beginning will produce rapidly escalating and compounding errors in the prediction of the system’s future behavior.”
It is hard to imagine a complex system that does not show sensitivity to initial conditions. If the follow-on statement is true, then there is little point to ever trying to model or predict the behavior of such a system because it is not predictable. But it is not hard to find counter-examples, even to the examples they provided. Meteorologists do a reasonable job predicting the weather; it depends on your standards of accuracy. Certainly they can predict fairly accurately the likelihood of a 90 degree day in January in Canada or anticipating the path of a tropical storm for the next 12 hours.
A less technical but perhaps more useful definition comes from membrane.com:
“A chaotic system is one in which a tiny change can have a huge effect.”
That leads us toward a more practical definition for our purposes.
For the types of systems we normally model, I would propose yet another definition.
A chaotic system is one in which it is likely that seemingly trivial changes in the initial conditions would cause significant changes in the predicted results, over the time frame being considered.
This definition, while not technically rigorous, acknowledges that most of us rarely have the opportunity or the need to deal in absolutes. We live in a world where the majority of decisions are made subjectively (“Joe has 20 years experience and he says…”) or with gross simplification (”Of course I can model that in a spreadsheet…”). In this world, being able to base a decision on a simulation model with better accuracy and objectivity can help realize tremendous savings, even if it is still only an approximation and only useful within specified parameters.
Can we accurately predict true chaotic systems? By strict definition clearly not. And even by my definition, there will be some systems that are just too chaotic to allow any predictions to be useful.
But can we provide useful predictions of most common systems, even those with some chaotic aspects? Absolutely yes. Every model is an approximation of a real or intended system. Part of our job as modelers is to ensure that the model is close enough to provide useful insight. A touch of chaos just makes that more interesting. 
Dave Sturrock
VP Products – Simio LLC
Tags: chaos, chaotic systems, process variability, simio, simulation software
I want to share a quotation about chaos:
“Where chaos begins, classical science stops” (James Gleick)
I definitely agree with you about the fact that simulation is useful, and as long as the modeler is attempting to make it as close as possible to the actual, it can provide useful insight.
I find that sometimes the biggest hurdle is getting the audience you’re doing the model for to understand that the simulation is indeed an approximation. This happens even in cases that are less likely to have chaos. In my world, I am amazed every day to the people in decision-making positions that take models as complete fact and hold you to it. I find myself repeatedly having to throw in caveats attempting to get the decision makers to understand that the model is the best it can be, but that it is as you said, an approximation. So one just has to be aware of potential short-comings in the model and do their best to paint as realistic of a picture as possible… even in the case of potential chaotic aspects.
I totally agree with this article. Like the “Butterfly Effect”: Small variations of the initial condition of a dynamical system may produce large variations in the long term behavior of the system(from Wikipedia). A tiny change can have a huge effect. But it’s the key point that how to find the tiny but important change?
And think from a different way, can we predict the effects and side-effects of making changes? Can we understand the potential impacts of process changes? Can we quantify the expected amount of improvements and benefits? I think those questions are the most interesting part attracts people to do simulation. Maybe more questions generated during the problem-solving process, but we try and find different ways to face every challenge.
This article reminds me the class project what we’re doing now.
We’re simulating a human body’s digestive system, which we found it’s very interesting, but very hard to do. Sometime I even doubt whether it’s gonna work.
Maybe anything related to a creature or some natural thing, like the earth, the weather, would be modeled at all, because I belive there’re some chaos about the nature which Human beings can not complete know forever, at least for now.
So if we’re gonna model a chaos system, whatever our reason and purpose is, maybe we should set a boundary of our system, we certinaly can not model all the logic inside of this chaos system, but we can model some part of it and ignore the others.
I guess we can just make benefit from some part of this chaos and get the results we want, and leave something we can not control along.