Passage time,resilience, and structure of compartmental models

The relation between the graphical structure and two measures of stability of a compartmental model is studied. The two are resilience as measured by deviation from equilibrium throughout the history of the system and mean first passage time from a central compartment back to itself. A number of examples are studied and a theory developed for models whose graphical structure is in the form of an advanced rosette. The resilience, known to increase with complexity, is shown to increase as well with uneveness in length of food chains. The mean first passage time, on the other hand, depends only on the number of food chains and their average length.