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|Subject: Re: Catastrophe theory, instability, risk||Date: 10/11/2012 5:10 AM|
|Author: LorenCobb||Number: 405769 of 472026|
From the NYT blog: A field known as catastrophe theory explores how slow continuous changes in the force applied to a system (like the gradually increasing load on a camel’s back) can trigger rapid discontinuous jumps in its response... What’s especially worrisome is that the jump occurs without warning. An intersection, by its very nature, doesn’t fade away. It exists until it doesn’t...
Yep. Some of us have been working on statistical means for detecting the potential for catastrophic behavior for decades. Here is one of my early papers on this very subject, from 1980:
My 1980 paper doesn't say so, but in fact it is not true that the jump occurs without warning. There are subtle changes in behavior that are detectable during the run-up to the catastrophic state transition. This is also true -- but harder to see -- in the "sandpile" instability described elsewhere in Wendy's post. The two types of instability are not at all the same, mathematically, but both are surpassingly fascinating from many points of view. As Wendy points out, catastrophe theory reminds us to be careful of unexpected behavior arising from nonlinear dynamics.
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