[time-nuts] simulation of interconnected clocks
Attila Kinali
attila at kinali.ch
Sun Dec 8 06:29:39 EST 2013
On Sat, 30 Nov 2013 06:31:01 -0800
Jim Lux <jimlux at earthlink.net> wrote:
> Recently, I've been looking at the variations of some human clocks which
> are millenia old: Galileo used his pulse as a timer for his famous "roll
> balls down a ramp" experimenet". I thought that some time-nuts might be
> interested in working with a clock that's a bit different than one
> depending on atomic vibrations, or motion within a crystal lattice.
I don't know whether this is of any help to you, but some time ago
i stumbled about some old lectures by Charles Peskin on the heart and
to its chaotic self-synchronization [1].
If you are interested in the synchronisation phenomena in biological
oscillators, i can recommend you [2].
Also a good read is [3] which gives a quite lengthy analysis on Kuramotos
model [4].
Also a nice review paper is [5], which starts from Kuramoto and explains
the current unsolved problems with coupled oscillators and their
mathematical description.
Attila Kinali
[1] "Mathematical aspects of heart physiology",
by Peskin, 1975
http://math.nyu.edu/faculty/peskin/heartnotes/index.html
[2] "Synchronization of Pulse-Coupled Biological Oscillators"
by Mirollo and Strogatz, 1990
http://math.bd.psu.edu/faculty/stevens/MATH497K/Papers/Syncrhonization.pdf
[3] "The Kuramoto model: A simple paradigm for synchronization phenomena",
by Acbron, Bonilla, Vincente, Ritort, Spigler, 2005
http://rmp.aps.org/abstract/RMP/v77/i1/p137_1
[4] "Self-entrainment of a population of coupled non-linear oscillators"
by Kuramoto, 1975
http://www.springerlink.com/content/71073361941277h8/
[5] "From Kuramoto to Crawford: exploring the onset of synchronization
in populations of coupled oscillators",
by Strogatz, 2000
http://www.sciencedirect.com/science/article/pii/S0167278900000944
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2.) Reduce to the essential.
3.) Stop and question.
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