The coordination dynamics of mobile conjugate reinforcement

What we know about infant learning and memory is founded largely on systematic studies by the late Carolyn Rovee-Collier (1942-2014) and her associates of a phenomenon called mobile conjugate reinforcement. Experiments show that when a ribbon is attached from a 3-month-old infant's foot to a mobile suspended overhead the baby quickly realizes it can make the mobile move. The mobile, which offers interesting sights and sounds, responds conjugately to the baby's vigorous kicks which increase in rate by a factor of 3-4. In this paper, using the concepts, methods and tools of coordination dynamics, we present a theoretical model which reproduces the experimental observations of Rovee-Collier and others and predicts a number of additional features that can be experimentally tested. The model is a dynamical system consisting of three equations, one for the baby's leg movements, one for the jiggling motion of the mobile and one for the functional coupling between the two. A key mechanism in the model is positive feedback which is shown to depend sensitively on bifurcation parameters related to the infant's level of attention and inertial properties of the mobile. The implications of our model for the dynamical (and developmental) origins of agency are discussed.