Article View: comp.theory.dynamic-sys
Article #232Re: Can Chaos Be Predictable?
From: Tom Scavo
Date: Fri, 21 Jun 1991 15:38
Date: Fri, 21 Jun 1991 15:38
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1287 bytes
In article <1991Jun20.194552.15875@cunews.carleton.ca> rdb@scs.carleton.ca (Robert D. Black) writes:
>I recently read that the chaotic logistic equation
>
> u(t+1) = 4u(t)(1-u(t)) u(0) in 0..1,
> t = 0,1,2,...
>has an ANALYTIC SOLUTION:
>
> u(t) = sin**2 (2**(t-1) arccos(1-2u(0)))
>
> Reference "Differential Equations" by Walter G. Kelly and
^^^^^^^^^^^^
> Alan C. Peterson, Academic Press 1991, p184.
A small correction: the title of the referenced book is
"Difference Equations" which can be guessed by the above
example. Just wanted to set the record straight...
--
Tom Scavo
scavo@cie.uoregon.edu
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Path: arc1-ca.pugleaf.net!utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!caen!spool.mu.edu!cs.umn.edu!ariel.unm.edu!cie.uoregon.edu!scavo From: scavo@cie.uoregon.edu (Tom Scavo) Newsgroups: comp.theory.dynamic-sys Subject: Re: Can Chaos Be Predictable? Keywords: chaos, predictability Message-ID: <1991Jun21.153833.24881@ariel.unm.edu> Date: 21 Jun 91 15:38:33 GMT Article-I.D.: ariel.1991Jun21.153833.24881 References: <1991Jun20.194552.15875@cunews.carleton.ca> Distribution: comp.theory.dynamic-sys Organization: Campus Information Exchange, University of Oregon Lines: 20