Wednesday, January 14, 2015

Global Synchronization of Oscillators in Nature

Global synchronization of oscillators is found abundantly in nature, emerging in fields from physics to biology. The Kuramoto model describes the synchronization behavior of a generalized system of interacting oscillators.

A particularly beautiful example comes from certain species of fireflies, with stories of huge populations of fireflies all flashing in perfect unison, making long swaths of light flashing on and off in the darkness. It was not until the late 1960s that anyone understood what was really going on—that the rhythm was not being set by any single “conductor” firefly, but rather by the interactions among all of them. Somehow the oscillator in each firefly (presumably some patch of neurons in each firefly’s brain) corrects itself to flash in unison with all the others.

With a large number of oscillators with different natural frequencies, the Kuramoto model predicts that, if they are allowed to interact strongly enough, they will all start oscillating at the same rate. The model provides a mathematical basis for studying the conditions under which synchronization can occur. For example, it is possible to solve for the critical amount of coupling needed among the oscillators to have synchronization. (Source: Synchronization of Globally Coupled Nonlinear Oscillators: the Rich Behavior of the Kuramoto Model by Bryan C. Daniels)

Here are some simulations I had run for the Kuramoto model using a Normal and a Cauchy-Lorentzian distribution as part of the Computational Biology 1 course in Complex Adaptive Systems at Chalmers Univ:

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