This article presents a formal mathematical model of child abuse based upon elementary catastrophe theory, a branch of differential topology. It was found that child abuse, when viewed as discontinuity in parent-child relations, could be successfully modeled by a five-dimensional butterfly catastrophe composed of four control parameters: stress, extrafamilial communication, attachment behavior, and parental history. Implications of the model for theory and research include: (a) emphasizing the role of communication in the etiology of abuse, (b) explanation of a wide array of seemingly contradictory findings, and (c) the generation of new research questions. On the basis of these findings, it is concluded that the butterfly model of abuse warrants further investigation.
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(Reprinted from D. Adamovicz, (ed.) Proceedings of the First National Conference on Child Abuse and Neglect, U.S. Department of Health, Education, and Welfare, 1976).
