Dynamical systems model of development of the action differentiation in early infancy: a requisite of physical agency

Young infants are sensitive to whether their body movements cause subsequent events or not during the interaction with the environment. This ability has been revealed by empirical studies on the reinforcement of limb movements when a string is attached between an infant limb and a mobile toy suspended overhead. A previous study reproduced the experimental observation by modeling both the infant's limb and a mobile toy as a system of coupled oscillators. The authors then argued that emergence of agency could be explained by a phase transition in the dynamical system: from a weakly coupled state to a state where the both movements of the limb and the toy are highly coordinated. However, what remains unexplained is the following experimental observation: When the limb is connected to the mobile toy by a string, the infant increases the average velocity of the arm's movement. On the other hand, when the toy is controlled externally, the average arm's velocity is greatly reduced. Since young infants produce exuberant spontaneous movements even with no external stimuli, the inhibition of motor action to suppress the formation of spurious action-perception coupling should be also a crucial sign for the emergence of agency. Thus, we present a dynamical system model for the development of action differentiation, to move or not to move, in the mobile task. In addition to the pair of limb and mobile oscillators for providing positive feedback for reinforcement in the previous model, bifurcation dynamics are incorporated to enhance or inhibit self-movements in response to detecting contingencies between the limb and mobile movements. The results from computer simulations reproduce experimental observations on the developmental emergence of action differentiation between 2 and 3 months of age in the form of a bifurcation diagram. We infer that the emergence of physical agency entails young infants' ability not only to enhance a specific action-perception coupling, but also to decouple it and create a new mode of action-perception coupling based on the internal state dynamics with contingency detection between self-generated actions and environmental events.

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.