Quantized orbits in weakly coupled Belousov-Zhabotinsky reactors

¹ Center for the Study of Complex Systems, University of Michigan - Ann Arbor, MI, USA
² Institute for Terahertz Science and Technology, University of California - Santa Barbara, CA, USA

Received: 2 February 2015
Accepted: 15 June 2015

Abstract

Using numerical and experimental tools, we study the motion of two coupled spiral cores in a light-sensitive variant of the Belousov-Zhabotinsky reaction. Each core resides on a separate two-dimensional domain, and is coupled to the other by light. When both spirals have the same sense of rotation, the cores are attracted to a circular trajectory with a diameter quantized in integer units of the spiral wavelength λ. When the spirals have opposite senses of rotation, the cores are attracted towards different but parallel straight trajectories, separated by an integer multiple of λ/2. We present a model that explains this behavior as the result of a spiral wavefront-core interaction that produces a deterministic displacement of the core and a retardation of its phase.