"Analysis of synchronization in a slowly changing environment: How slow coupling becomes fast weak coupling"
Physical Review Letters, 110:204101
Mouse over here for a brief summary or click to open article in a new tab.Many physical systems strongly interact with their environments: the environment affects their behavior, while their behavior in turn alters the environment. If multiple animals, cells, or other units co-exist in the same environment, then they may influence each other indirectly through their effects on their common environment. This paper presents a new, general mathematical approach that we developed for analyzing how these indirect interactions can promote or prevent coordination of the units involved. The method applies to physical systems of components with two ingredients: (1) on their own, the components oscillate in time (that is, some aspect of the system rises and falls, repeatedly, over time), and (2) the components interact through an external medium or environment that changes gradually. Examples of such systems include neurons with oscillations in their membrane potentials (what neurons use to send signals to other neurons) that share an external ion pool (since neuronal oscillations require these ions), particularly in settings with high neuronal activity levels such as epilepsy; bacteria with internal oscillations in gene expression that live in a common medium; or predator-prey pairs living in a common ecosystem (e.g., stoats and songbirds, owls and insects in the woods).