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|Subject: Catastrophe theory, instability, risk||Date: 10/9/2012 2:13 PM|
|Author: WendyBG||Number: 405636 of 504765|
By STEVEN STROGATZ
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....
...intersections [between a line and a curve] often represent answers. Solutions. States of equilibrium. In mathematical models of economies, or ecosystems, or other kinds of dynamical systems, intersections are where variables come to rest and settle down. In economic models, for example, the equilibrium price of an item is set by the intersection of supply and demand curves. If that intersection suddenly vanishes, the price has to jump.
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...
....the “fold catastrophe” is the most basic scenario in catastrophe theory. It’s important because in its aftermath there are no other intersections in sight. Whatever the system is going to do next, it’s going to be something radically different. It has to leap to a different state.... [end quote]
This article reminds me of the striking, memorable 2006 article by John Mauldin:
Fingers of Instability
By John Mauldin
August 25, 2006
This week we revisit some ideas on how change occurs. We are in a transition in the world economy, and it sometimes helps to think about how these transitions take place. What is the mechanism for change? Can we see it coming soon enough to avoid the problems and take advantage of them? ...
How Change Happens
By John Mauldin
August 17, 2012
Imagine, Buchanan says, dropping one grain of sand after another onto a table. A pile soon develops. Eventually, just one grain starts an avalanche. Most of the time it is a small one, but sometimes it builds on itself and it seems like one whole side of the pile slides down to the bottom.
They learned some interesting things [about nonequilibrium systems]. What is the typical size of an avalan