The application of vector envisionment to compartmental systems

Vector envisionment (VE) is a qualitative modelling method, for reasoning about dynamic physical systems, based on qualitative vectors. An envisionment is the set of all possible qualitative behaviours that a system may exhibit for a particular input. Compartmental systems are a class of dynamic system composed of a finite set of homogeneous, well mixed, lumped subsystems called compartments; the behaviour of each compartment may be described by a first order differential equation. It is demonstrated that, for a linear time invariant compartmental system, VE can find all the distinct qualitative states in which the system may exist for a given input. From these a solution space is constructed which is divided in accordance with the critical points of the system. Each qualitatively distinct region of this space is associated with a particular range of magnitudes for the initial values for the state variable. An envisionment graph is also produced which, combined with the solution space, gives a means of overcoming the problem of chattering.