Friday, 10 August 2012

Stability, Feedback and Tipping Points - (Part 3)

These days, Tipping Point is frequently used in discussions to describe a point of no return or a point of sudden and large change.
The change may be undesirable, catastrophic, unpleasant, unplanned, unexpected or irreversible.
Alternately the change may be sought for, as in marketing a product, or in social media to generate a lot of contacts. 

Stable systems return to their normal state of stability after they are  disturbed slightly by an external agent;  Remember the example of a marble in a bowl  Negative Feedback

However, if the marble is pushed more and more until it reaches the top of the bowl,  then a slight further push will take it to a new state from where it can not return to the original state.
The marble has passed the tipping point.  Beyond the tipping point, there may be a new state of stability, as shown in the diagram, or there may be a precipice, cliff edge – a point implying catastrophe.

Small changes can build up to bring a system to a state (tipping point) that even a further small change can cause large and irreversible shift in the state of the system. 

The pressures that human activities are placing on the Earth's ecosystem are increasing and we may be reaching a tipping point when serious undesirable and damaging changes to the ecosystem become inevitable. 
Earth is rapidly approaching a tipping point
Ecosystem collapse?

When the tipping point happens is difficult to predict.  In a complex system with many parameters it is not possible to exactly say when the system will switch to a new stable state or collapse.  One looks for signs of stress and forms an opinion about the future behaviour of the system.

A good read is Malcolm Gladwell's book in which he describes The Tipping Point as that magic moment when an idea, trend, or social behaviour crosses a threshold, tips, and spreads like wildfire. Just as a single sick person can start an epidemic of the flu, so too can a small but precisely targeted push cause a fashion trend, the popularity of a new product, or a drop in the crime rate.  He describes several examples such as a New Yorker district which becomes more and more dangerous because of small changes such as broken windows which convey the message to people that the neighborhood became less caring.

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