Hi
Yes, the "settling in" is fractal and the path taken to sync isn't the same
every time.
For a "simple" way to look at multiple coupled clocks go back to old style
filter theory:
1) You have some number of resonators
2) You have some set of coupling coefficients between the resonators
3) You get a multi way transfer function between them
4) The Q of the resonators is very high ("Infinite Q")
5) The coupling is small, but maybe not small compared to the infinite Q.
All you need for an oscillator is a net zero phase around the loop and gain. If
you have multiple phase zeros (think of a complex filter) then there are
multiple solution frequencies. The ones that will work are the ones with gain.
Something like a metronome has trouble running at several frequencies at once,
so it picks one. The system also can have too little coupling (not enough gain)
to sync and things just run off on their own.
Yes the analogy to filters isn't perfect. There are more accurate ways to look
at it.
Bob
On Sep 14, 2013, at 8:32 AM, Tim Shoppa <tsho...@gmail.com> wrote:
> Coupled oscillators can do very interesting things above and beyond simple
> synchronization.
>
> Look at the circuit at the bottom of this page with 5 cross-connected neon
> bulb multivibrators. http://donklipstein.com/sillyne2.html They are
> symmetrically cross connected favoring no particular direction. After
> powering up, they flash in a disorganized manner for a little bit, but then
> usually settle down into either a left-to-right or right-to-left sequence.
> I think this is "spontaneous symmetry breaking".
>
> They don't always settle down quickly. I have observed some other cycles at
> power-up that are more complex, and can run for many seconds before they go
> into the simple sequence.
>
> Tim.
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