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Understanding spatiotemporal complexity1, 2, 3 is important to many disciplines, from biology4, 5 to finance6. However, because it is seldom possible to achieve complete control over the parameters that determine the behaviour of real complex systems, it has been difficult to study such behaviour experimentally. Here we demonstrate a simple microfluidic bubble generator that shows stable oscillatory patterns (both in space and time) of unanticipated complexity and uniquely long repetition periods. At low flow rates, the device produces a regular stream of bubbles of uniform size. As the flow increases, the system shows intricate dynamic behaviour typified by a stable limit cycle of order 29 bubbles per period, which repeats without change over intervals of up to 100 periods and more. As well as providing an example of a well-characterized and experimentally tractable model system with which to study complex, nonlinear dynamics, such behaviour demonstrates that it is possible to observe complex and stable limit cycles without active external control.

Oscillations with uniquely long periods in a microfluidic bubble generator