Philip Ball finds out how two ticking clocks can stop each other dead.
Clocks, cells and other oscillating systems can bring one another to a halt, a team of physicists in India announces in the journal Physical Review Letters1. This could have implications from medicine to information technology.
Two pendulum clocks hung from a wooden plank next to one another can keep time in exact synchrony, thanks to weak vibrations transmitted through the plank.
Such 'coupled oscillators' also crop up in biological contexts. Swarms of fireflies in a tree gradually synchronize their on-off flashes, until the entire tree is flashing as though wreathed in fairy lights. Crickets chirps get in step, creating a precisely orchestrated warble. There is some evidence that the rhythms of human breath and heartbeat are coupled.
Certain kinds of coupled oscillators -- 'limit-cycle oscillators' -- can also stop one another dead, Abhijit Sen and colleagues at the Institute for Plasma Research in Bhat, India, now demonstrate. They name this phenomenon, which they predicted theoretically in 1998, 'amplitude death'2.
Limit-cycle oscillators are ones that will oscillate of their own accord, without an external driving force. The pacemaker cells that set the rhythms of the heart are like this, as are pendulum clocks with an escapement (which permits the pendulum to swing in only small oscillations).
The key condition for amplitude death is that it takes time for the influence of one oscillator to reach the other. Previous researchers have tended to sweep this delay under the carpet. The equations for coupled oscillators were already hard enough to solve, and with a time delay included, they became almost impossible.
In 1998 Sen and colleagues made some theoretical predictions about the effects of a delay by simplifying their mathematical assumptions about coupled oscillators. They found that for certain ranges of both the time delay and the strength of the coupling, a pair of oscillators could drag each other to a standstill. They called these regions 'death islands'.
Now Sen's group have linked two electrical oscillator circuits with a delay line, and watched them wobble. As they scanned across the range of delays and coupling strengths, they saw the synchronized oscillations vanish. They also saw other kinds of unusual behaviour, such as antiphase locking -- where the oscillators tick perfectly out of step, like clocks swinging their pendulums in opposite directions.
Understanding amplitude death is important for electronic engineers who seek to amplify banks of lasers by coupling the oscillations of the laser light. Under the wrong circumstances this could switch the lasers off rather than make them brighter. And there might be medical implications too, for devices that regulate heartbeats.
RamanaReddy, D. V., Sen, A. & Johnston, G. L. Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators. Physical Review Letters 85, 3381 - 3384 2000.
RamanaReddy, D. V., Sen, A. & Johnston, G. L. Time-delay-induced death in coupled limit cycle oscillators. Physical Review Letters 80, 5109 - 5112 1998.
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Ball, P. Islands in the swing. Nature (2000). https://doi.org/10.1038/news001012-5