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Qualitative theory of compartmental systems. (English) Zbl 0776.92001

Dynamic models of many processes in pharmacokinetics, metabolism, epidemiology, ecology and other areas are derived from mass balance considerations. These models lead to particular systems of ordinary differential equations, that are called compartmental systems.

The authors review the qualitative results on nonlinear compartmental systems and present a unified and simplified theory for such systems. They also present an overview on the theory of linear compartmental systems. Finally, they show how to partition compartmental systems of arbitrary connectivities into four basic types and give a qualitative analysis for autonomous nonlinear compartmental systems of the four basic types.

Reviewer: S.Anita (Iaşi)

MSC:
92B05General biology and biomathematics
93A30Mathematical modelling of systems
37-99Dynamic systems and ergodic theory (MSC2000)
37N99Applications of dynamical systems
93A99General systems theory