Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 9, Iss. 4, October, 2005, pp. 479-503
@2005 Society for Chaos Theory in Psychology & Life Sciences

 
 
 

Identifying Ill-Behaved Nonlinear Processes Without Metrics: Use of Symbolic Dynamics

Robert A. M. Gregson, Australian National University

Abstract: Given ill-behaved psychological data that are unlikely to satisfy metric axioms, the use of encoding in symbolic dynamics, and hence leading into Markov analyses, is explored. Various measures of entropy are calculated. The tractability of entropic measures for categorizing the trajectories of nonlinear dynamics that may be present and chaotic is considered, with a focus on the case where there are two attractors and at least one heteroclinic orbit between them. Fast/slow dynamics are treated as a special case. The problem of identification is in other contexts the problem of diagnosis in time-varying pathologies. Some real data, selected for their psychological relevance in clinical, forensic and psychophysical processes, that are apparently edge-of chaos and nonstationary, are for comparison analysed both as metric and discrete and in symbolic encoding.

Keywords: identifiability, psychometrics, nonstationarity, chaos, entropy, Markov, symbolic dynamics, two attractors