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From: guy@physics (Guy Metcalfe)
Newsgroups: comp.theory.dynamic-sys,sci.math,sci.physics
Subject: Re: Intermittency
Message-ID: <22050@duke.cs.duke.edu>
Date: 8 Mar 91 03:11:47 GMT
References: <1991Mar1.001103.6341@cec1.wustl.ed> <1991Mar6.232931.2553@agate.berkeley.edu>
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In article <1991Mar6.232931.2553@agate.berkeley.edu> william@ronzoni.berkeley.edu (W. E. Grosso) writes:
>and presentation. The question : does anybody out there
>know about intermittency in dynamical systems 
>(from what I gather, it seems to be associated with 
>numerical experimentation).

There are indeed numerical experiments using 1- and 2-dimensional maps
that exhibit intermittent behavior, but by no means is the phenomena
so limited: it is observed in certain systems of differential
equations, and in the lab.  I am most familiar with examples from
convection experiments, and, while these are the most well explored,
there are other example systems.

There are in fact 3 types of `classical' intermittency that are
distinguished by how eigenvalues leave the unit circle in the complex
plane.  These were first discussed in

\bibitem{Poman}
Y. Pomeau and P. Manneville, Commun. Math. Phys. {\bf 74}, 189 (1980).

and examples observed in convective systems by, among others,

\bibitem{intermittency_folk}
P. Berg\'e, M. Dubois, P. Manneville, and Y. Pomeau, J. Phys. (Paris)
Lett. {\bf 41}, L341 (1980); M. Dubois, M. A.  Rubio, and P. Berg\'e,
Phys. Rev. Lett. {\bf 51}, 1446 (1983); H.  Haucke, R. E. Ecke, Y.
Maeno, and J. C.  Wheatley, Phys. Rev. Lett.  {\bf 53}, 2090 (1984).

The recent book by Manneville ("Dissapative Structures and Weak
Turbulence" Academic Press, 1990?) has good discussion and more
references.

Lately, other types of intermittency associated with chaotic dynamics
have been explored.  I'm thinking of the work by Grebogi, Ott, Yorke
and coworkers at Maryland.  Some references are

\bibitem{goy}
Celso Grebogi, Edward Ott, Filipe Romeiras and James A. Yorke, Phys.
Rev. A {\bf 36}, 5365 (1987); Celso Grebogi, Edward Ott and James A.
Yorke, Physica {\bf 7D}, 181 (1983); Phys. Rev. Lett. {\bf 48}, 1507
(1982).

This intermittency occurs as (chaotic) attractors collide with
manifolds of other objects in phase space, and then are
modified/destroyed by the interaction.  Read the references to find
out what really is thought to happen:-).  Some lab examples are

\bibitem{experiment_eg}
M. Iansiti, Qing Hu, R. M. Westervelt, and M. Tinkham, Phys. Rev.
Lett. {\bf 55}, 746 (1985); Didier Dangoisse, Pierre Glorieux, and
Daniel Hennequin, Phys. Rev.  Lett. {\bf 57}, 2657 (1986); T. L.
Carroll, L. M. Pecora, and F. J. Rachford, Phys. Rev.  Lett. {\bf 59},
2891 (1987); W. L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H.
Hsu, E. Kostelich, E. Ott, H. T. Savage, R. Segnan, M. L. Spano, and
J. A. Yorke, Phys. Rev.  Lett. {\bf 63}, 923 (1989).

And as you might guess from the bibliography entries, I plan to add to
the list of experimental examples shortly.

Hope your talk goes well and this info is helpful.
--
	Guy Metcalfe				
	Duke University Dept. of Physics	guy@phy.duke.edu
	& Center for Nonlinear Studies		guy@physics.phy.duke.edu
	Durham, N.C.      27706			guy%phy.duke.edu@cs.duke.edu