| Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 15, Iss. 4, Oct, 2011, pp. 465-476 @2011 Society for Chaos Theory in Psychology & Life Sciences Orbital Decomposition for Ill-Behaved Event Sequences: Transients and Superordinate Structures Abstract: Time series analysis is often challenged by the presence of transient functions.
We examined some types of transients found in time series of events that lend themselves
to symbolic dynamics analysis through the method of orbital decomposition, which is based
on the principle that chaotic series arise from coupled oscillators. Synthetic data sets
were constructed to study the impact of intrusive events, intrusive series, merged
functions, non-coupled oscillators, and driving oscillations on the patterns of final
statistics obtained from orbital decomposition analysis. Two real-world data sets - a
logbook of the ritual behaviors of a patient with obsessive compulsive disorder and a
time series of kill dates from an infamous serial murderer - were examined for non-ergodic
properties similar to those found in the synthetic data. Keywords: orbital decomposition, oscillator, symbolic dynamics, time series, transients, obsessive-compulsive disorder, serial murderer |