QUALITATIVE THEORY OF COMPARTMENTAL-SYSTEMS

Dynamic models of many processes in the biological and physical sciences which depend on local mass balance conditions give rise to systems of ordinary differential equations, many nonlinear, that are called compartmental systems. In this paper, the authors define compartmental systems, specify their relations to other nonnegative systems, and discuss examples of applications. The authors review the qualitative results on linear and nonlinear compartmental systems, including their relation to cooperative systems. They review the results for linear compartmental systems and then integrate and expand the results on nonlinear compartmental systems, providing a framework for unifying them under a few general theorems. In the course of that they complete the solution of a problem posed by Bellman and show that closed nonlinear, autonomous, n-compartment systems can show the full gamut of possible behaviors of systems of ODEs. Finally, to provide additional structure to this study, the authors show how to partition compartmental systems of arbitrary connectivities into four basic types and then give the qualitative analysis for autonomous, nonlinear compartmental systems of the four basic types.