Models of knowing and the investigation of dynamical systems

We present three distinct concepts of what constitutes a scientific underst anding of a dynamical system. The development of each of these paradigms ha s resulted in a significant expansion in the kind of system that can be inv estigated. In particular, the recently-developed 'algorithmic modelling par adigm' has allowed us to enlarge the domain of discourse to include complex real-world processes that cannot necessarily be described by conventional differential equations. (C) 1999 Elsevier Science B.V, All rights reserved.