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This study reports on a new dynamic systems method for studying infant socioemotional development, using conventional statistical techniques to portray dynamic systems constructs. State space grids were constructed from two ordinal variables, distress intensity and attention to mother, and hypothetical attractors were identified as grid cells with high cumulative duration of behavior. Attractor and state space characteristics were operationalized and tested, first to assess the utility of the method and second to reconceptualize and extend conventional developmental hypotheses. The basin strength and relaxation time of hypothetical attractors demonstrated their ‘attractiveness’ and predicted consistency in attractor location across sessions. Developmental changes and individual continuities in the organization of behavior were also revealed, in ways that would be inaccessible to conventional research methods.