FROM CONTINUOUS DYNAMICS TO SYMBOLS
HERBERT JAEGER · Studies of nonlinear phenomena in life science · 1999
This article deals with mathematical models of discrete, identifiable, "symbolic" events in neural and cognitive dynamics. These dynamical symbols are the supposed correlates of identifiable motor action patterns, from phoneme utterances to restaurant visits. In the first main part of the article, models of dynamical symbols offered by dynamical systems theory are reviewed: attractors, bifurcations, spatial segregation and boundary formation, and several others. In the second main part, transient attractors (TA's) are offered as yet another mathematical model of dynamical symbols. TAs share with ordinary attractors a basic property, namely, local phase space contraction. However, a TA can disappear almost as soon as it is created, which could (not very rigorously) be interpreted as a bifurcation induced by quickly changing control parameters. Such "fast bifurcation sequences" standardly occur in neural and cognitive dynamics. 1 Introduction This paper is about symbols, viewed as ide...