They are trying to model the periodic frequency with which serial killers strike.
Stochhastic modeling of a serial killer (pdf)M.v. Simkin and V.P. Royschowdhury (hat tip: NC)
We analyze the time pattern of the activity of a serial killer, who during twelve years had murdered 53 people. The plot of the cumulative number of murders as a function of time is of “Devil’s staircase” type. The distribution of the intervals between murders (step length) follows a power law with the exponent of 1.4. We propose a model according to which the serial killer commits murders when neuronal excitation in his brain exceeds certain threshold. We model this neural activity as a branching process, which in turn is approximated by a random walk. As the distribution of the random walk return times is a power law with the exponent 1.5, the distribution of the inter-murder intervals is thus explained. We confirm analytical results by numerical simulation.
They do not that a delay has to be built into the cycle, as the killer generally takes time to plot and plan once the necessary level of homicidal urges are reached. The killer then goes on a killing spree until the urges are satisfied.
I have my doubts that you will bring this down to a predictive level specific enough to individuals that it would be useful to the police.
I also suspect that most of the “serial” killers, never get serialized because they are caught. The notorious killers we know of are the ones that through some combination, of caution, skill, and (probably mostly) luck are able to keep going at it for some time.
However, as one commentator noted, using statistical methods is far better than using the hocus pocus of behavioral profiling.