I once came across a Wikipedia page describing a system where

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Apteronotus
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I once came across a Wikipedia page describing a system where indifferent of the initial starting position, at some final time t=T the system would always reach the same equilibrium position.

Does anyone know what the name of such a system is?

I recall there was an animation of 4 balls each starting at different heights on the same ramp at t=0 and at t=T the balls were always at the same height on the ramp.
 
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Hi Apteronotus! :smile:

I think that's an attractor …

see http://en.wikipedia.org/wiki/Attractor" :wink:​
 
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It would have to be an attractor with some kind of damping, otherwise you would get oscillatory motion around the equilibrium point. You could also call it a potential minimum