Editing Chaos theory (section)

==Introduction==
Chaos theory concerns deterministic systems whose behavior can, in principle, be predicted. Chaotic systems are predictable for a while and then 'appear' to become random. The amount of time for which the behavior of a chaotic system can be effectively predicted depends on three things: how much uncertainty can be tolerated in the forecast, how accurately its current state can be measured, and a time scale depending on the dynamics of the system, called the [[Lyapunov time]]. Some examples of Lyapunov times are: chaotic electrical circuits, about 1 millisecond; weather systems, a few days (unproven); the inner solar system, 4 to 5 million years.<ref>{{Cite journal|last1=Wisdom|first1=Jack|last2=Sussman|first2=Gerald Jay|date=1992-07-03|title=Chaotic Evolution of the Solar System|journal=Science|language=en|volume=257|issue=5066|pages=56–62|doi=10.1126/science.257.5066.56|issn=1095-9203|pmid=17800710|bibcode=1992Sci...257...56S|hdl=1721.1/5961|s2cid=12209977|hdl-access=free}}</ref> In chaotic systems, the uncertainty in a forecast increases [[Exponential growth|exponentially]] with elapsed time. Hence, mathematically, doubling the forecast time more than squares the proportional uncertainty in the forecast. This means, in practice, a meaningful prediction cannot be made over an interval of more than two or three times the Lyapunov time. When meaningful predictions cannot be made, the system appears random.<ref>''Sync: The Emerging Science of Spontaneous Order'', Steven Strogatz, Hyperion, New York, 2003, pages 189–190.</ref>