Modelling of Continuous Time Dynamic Systems

Abstract

This first chapter of Part III examines the conceptual modelling task within the context of continuous time dynamic systems (CTDS). It is noted that in contrast to the inductive process that prevails in the development of conceptual models in the DEDS domain, CTDS conceptual models generally emerge from a deductive process based on physical laws that are often (but not always) known to govern the behaviour of the SUI. Consequently in these circumstances, uncertainties about the relevant behaviour mechanisms within the SUI are therefore largely circumvented (assuming the knowledge of a domain expert is available). A second notable difference in conceptual model development in the CTDS domain (relative to the DEDS domain) is the absence, in many situations, of random effects. This circumvents the often challenging task of data model formulation and allows for a far simpler context for evaluation of the outcomes of simulation experiments. For the most part, CTDS conceptual models are formulated in terms of differential equations (while these could include both ordinary and partial differential equations, only the former are considered in the discussions). Several examples are presented to illustrate CTDS conceptual model development. Included is an example to illustrate a deductive rather than an inductive circumstance (predator/prey interaction). For the most part, the solution engine involved in carrying out experiments with CTDS models is a numerical procedure for solving the differential equations of the conceptual model. Many such procedures are available in the numerical mathematics literature and all generally require that the conceptual model be presented in a particular (canonical) form; namely as a set of first order differential equations. A transformation to this form is often necessary and this process is outlined.