There are N variables and K parameters. The number of dynamic variables of a system is known as the dimensionality of the system. The logistic map, for example, has dimensionality equal to one. Here there are two dynamic variables and four parameters. The model also illustrates why we think that memory performance may be profitably modeled by a nonlinear system.
Memory typically involves competition, and is limited in capacity, at least in working memory.
In addition to the van Geert work already cited, in recent years dynamic models have been proposed across psychology. See the reference list for a partial listing of this new work. One of the remarkable recent achievements in the study of nonlinear dynamics is the development of techniques for estimating dimensionality from measures on a single variable. Such techniques could be enormously useful to the model builder because they estimate the total number of dynamic variables needed to model the dependent variable. The major technique involves the embedding dimension , which is defined in terms of successive N-tuples of the time series data.