From continuous dynamics to symbols

This article deals with mathematical models of discrete identi able symbolic events in neural and cognitive dynamics These dynamical symbols are the sup posed correlates of identi able motor action patterns from phoneme utterances to restaurant visits In the rst main part of the article models of dynamical symbols o ered by dynamical systems theory are reviewed attractors bifurca tions spatial segregation and boundary formation and several others In the second main part transient attractors TA s are o ered as yet another mathe matical 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