Discontinuities in the Endogenous Change of Settlement Pattern

Publisher Summary This chapter discusses discontinuities in the endogenous change of settlement pattern. The simplest reasonable hypotheses on the economic use of land in agriculture and on the benefits of living in aggregated communities among differently dispersed nonurban populations are used to generate a model that predicts sudden shifts between a landscape of scattered farmsteads and one of nucleated villages as a result of smooth changes in factors such as soil fertility and farming technique. The model presents an analysis that offers an explanation of discontinuous change in terms of continuously changing variables. The approach can be extended beyond the analysis of settlement size to that of shifts in settlement location. The model brings out the importance of a class of stable phenomena called constraint catastrophes, which govern stable bifurcation at a boundary for nonlinear optimization problems that are constrained by inequalities. The possible bifurcation behaviors are significantly different from the seven elementary catastrophes but may be classified and analyzed by the same methods.