analogies between josephson junction linkage and huygens coupled pendulums

October 24, 2015

In 1665, Christiaan Huygens [Huygens, 1673] noted “When we suspended two clocks so constructed from two hooks imbedded in the same wooden beam, the motions of each pendulum on opposite swings were so much in agreement that they never receded the least bit from each other and the sound of each was always heard simultaneously. Further, if this agreement was disturbed by some interference, it reestablished itself in a short time. For a long time I was amazed at this unexpected result, but after a careful examination finally found that the cause of this is due to the motion of the beam, even though this is hardly perceptible. The cause is that the oscillations of the pendula, in proportion to their weight, communicate some motion to the clocks. This motion, impressed onto the beam, necessarily has the effect of making the pendula come to a state of exactly contrary swings if it happened that they moved otherwise at first, and from this finally the motion of the beam completely ceases.” The study of coupled
oscillators has since become an active branch of mathematics, with applications in physics, biology, and chemistry. In physics, one encounters coupled oscillators in arrays of Josephson junctions [Chung et al., 1989, Blackburn et al., 1994], in modelling molecules [Sage, 1994], and in coupled lasers [Dente et al., 1990]. Coupled oscillators are also prevalent in biological systems. Most organisms appear to be coupled to various periodicities extant in our surroundings, such as the rotation of the earth about the sun, the alternation of night and day, or the tides. Not only do organisms exhibit periodicities due to their environment, but they also exhibit innate periodic behavior. Breathing, pumping blood, chewing, and galloping are examples of rhythmic patterns of motion…