Many of the problems our society faces are concerned with large, complex, and difficult-to-understand systems. This is true of problems involving energy supply and demand, food supply, transportation, pollution, urban services, health care, and so on. The application of mathematical techniques, so frequently successful in dealing with small, well-defined, and mechanistic physical or engineering problems, is not always very helpful in dealing with these more complex systems. However, mathematics has a role to play, if we are more modzst in what we expect to learn about a system whose behavior is being studied mathematically. In this paper, we shall describe some techniques which are part of a general approach to the study of complex systems known as structural modeling. In structural modeling, we concern ourselves mostly with qualitative predictions about systems. We are mostly interested in learning about “geometric” properties of these systems, properties which describe their type of growth, their stability or instability, their sensitivity, and so on, in qualitative terms: they grow without bound, they oscillate wildly, etc. More specifically, we are interested in relating these qualitative properties of a system to certain structural properties of the system. Techniques of structural modeling have been applied to such diverse problems as energy use, air pollution, and transportation systems,’z*22-27*29 health care delivery, water policy, and environmental policy,7-’o naval manpower,” the analysis of coastal resources and the transportation of coal in inland and the study of ecosystem^.'^"^ Recent surveys of structural modeling have been carried out by Cearlock? and Lendaris and Wakeland.I3 We shall concentrate on the technique of pulse process analysis developed by R ~ b e r t s , ~ ’ ~ ~ and Roberts and and generalized by McLean16 and McLean and We shall solve some of the problems posed in Robertsz4 and extend some of the results of Roberts and Brown.29 We shall discuss applications of pulse process analysis to problems of health care delivery, energy use in food production, and transportation.
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