Imperfect Symmetry and the Elementary Coordination Law

The ability to synchronize rhythmically moving limbs and limb segments is one of the most fundamental abilities of vertebrate and invertebrate movement systems. As Kelso [18] has underscored, the ability is a primary expression of how movements (a) are organized in space and time, (b) resolve issues of efficiency, and (c) meet the competing challenges of stability and flexibility. In broad theoretical terms, 1:1 frequency locking of two or more limb segments is one of biology’s original models for collective behavior — the organizing of multiple interactions among neural, muscular, metabolic, and mechanical processes under task-specific intentional constraints. Given the complexity, the task of formulating and validating quantitative mathematical models of monofrequency rhythmic coordination based on physicochemical principles, neurobiological facts, and assumptions about intentionality has proven to be extremely difficult and may well be intractable. An alternative approach, the one adopted more than two decades ago by Haken, Kelso, and Bunz [15], attempts to develop a qualitative dynamical model that incorporates, in broad strokes, the essential features of synchrony between and among the components of, in principle, any biological movement system. The model-independent approach taken by Kelso and his colleagues accords with elementary lessons from the study of complexity [11].