Bifurcation and Disaggregation in Lowry—Garin Derivative Models: Theory, Calibration, and Case Study

The classic Lowry—Garin model is reexamined in light of advances in bifurcation theory and disaggregate model calibration techniques. A procedure for disaggregate calibration of the multipliers used in the economic-base component of the model is presented. Also given is an endogenous calibration procedure to include zonal constraints into the spatial interaction part of the unconstrained Lowry—Garin model. This is accomplished through the use of only two simple parameters which have important physical interpretations regarding the sensitivity of transportation improvements. Bifurcation conditions are then specified for the constrained model in both the aggregate and disaggregate cases. Through a case study of a medium-size city, the disaggregate calibration approach was found to produce better replication of the observed development pattern. Also the endogenous way of embedding zonal constraints in the two aforementioned parameters was found to be extremely efficient computationally. Most importantly, the analytical framework offers a transparent way of explaining urban development, including the prediction of precipitous developments, thus relieving much of the burden of traditional simulation approaches which tend to be cumbersome and analytically intractable.