The Butterfly Effect

blue_morpho_butterfly_large.jpgCan a butterfly flapping it’s wings can cause a hurricane?

Well, maybe. Really complex systems like the weather and ecosystems are pretty, well, complex. (How my wife drives is also a complex system but so far has resisted any scientific understanding.)

The butterfly effect is simply this: Any change in the initial conditions of a complex non-linear system creates wildly different outcomes.

A more technical description would be: sensitive dependence on initial conditions in chaos theory where small variations of the initial condition of a nonlinear dynamical system produce increasingly large variations in the long term behavior of the system. Whew.


The phrase The Butterfly Effect refers to the idea that the single flap of a butterfly’s wings change the initial conditions of the system enough to cause large-scale phenomena (hurricanes and such) since any variation in the initial conditions is vastly magnified with each iteration. And every flap of every butterfly wing in the world continually changes those conditions. (Someone passing gas in France probably caused the Katrina hurricane.) Now you know why you don’t want to be a weatherman. It basically means that we’ll never be able to predict the weather for more than a few days.

butterflyeffect

eq.butterflyeffect.png 

See that equation? Looks tricky doesn’t it? You can’t understand how my wife drives either.

Comparing the butterfly effect to the domino effect is slightly misleading. In the domino effect there is dependence on the initial sensitivity, but whereas a simple linear row of dominoes would cause one event to initiate another similar one, the butterfly effect amplifies the condition upon each iteration. Also, dominos are a game played by old people in Miami.


Animal populations can be subject to the same phenomena.


Predator-prey systems have complex dynamics. A bio system with two variables such as rabbits and foxes can create a system that is much more complex than is readily apparent. Lack of foxes means that the rabbit population can increase, but increasing numbers of rabbits means foxes have more food and are likely to survive and reproduce, which in turn decreases the number of rabbits.

So please, don’t pass gas. Forecasting the weather is hard enough.