A Cusp Catastrophe Approach to the Prediction of Temporal Patterns in the Kill Dates of Individual Serial Murderers

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.     

Modeling Maher's Attribution Theory of Delusions as a Cusp Catastrophe

Maher's (1974, 1988) attribution theory of delusions was reformulated as a cusp catastrophe model and tested using 193 percipients' paranormal beliefs, paranormal experiences, and fear of the paranormal as measured by Kumar et al.'s (1994) Anomalous Experiences Inventory, and their tolerance of ambiguity as measured by McDonald's (1970) AT-20. The magnitude of the difference between percipients' fear and belief was used as the dependent variables, whereas experience and tolerance of ambiguity were used as asymmetry and bifurcation variables, respectively. Using the GEMCAT II software it was shown that this cusp provided a superior fit to the data than competing linear, fold, and cusp models. Consistent with Maher's formulation, two basic states were found to exist: one in which fear dominates belief, and a second in which belief dominates fear. Further, fear of the paranormal increased with greater intolerance of ambiguity while belief decreased with increasing tolerance. The model explains why paranormal beliefs are resistant to change in the face of counterargument or contradictory evidence.