| Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 3, Iss. 2, Apr, 1999, pp. 143-159 @1999 Society for Chaos Theory in Psychology & Life Sciences A Cusp Catastrophe Approach to the Prediction of Temporal Patterns in the Kill Dates of Individual Serial Murderers Abstract: A cusp catastrophe model was fitted to the time series of kill dates of eleven serial murderers, using no additional external information. As predicted, this model provided a superior fit (Median R2 = 0.67) to the data than competing linear models (Median R2 = 0.43 and 0.22). Moreover, a single equation could be identified which was moderately effective (R2 = 0.53) in predicting the changes in the intervals between successive killings across individual killers. All time series showed evidence for the existence of a cyclic underlying process, although distinctions could be made depending on whether the phase portrait showed an attractor, a repellor, or a "pulse" type pattern. Finally, using a neural net approach it proved possible to distinguish pairs of serial killers solely based on properties of their time series. These findings are best explained by biological theories which assume that the cyclic nature of serial murder is the result of the successive domination of opposing forces. Keywords: serial murderers, cusp catastrophe, Lyapunov dimension, criminal behavior, phase portrait |