Complementary levels of description in applied mathematics. III: Equilibrium models of cities (Q1113846)

[Part I and II of this paper dealt with different topics and appeared in Int. J. Math. Educ. Sci. Technol.] The paper summarizes \textit{J. A. Amson}'s approach to city equilibrium and growth models [see Envir. Plann. 4, 429-444 (1972) and ibid. 5, 295-338 (1973)], mainly its philosophy and methodology. It aims to illustrate the processes and levels of description in mathematical modelling and to present a base to a course in advanced modelling. After an introduction and definitions, the author discusses consequences of the axiom of circular symmetry and states a number of lemmas and theorems arising from the axiomatic model. As a rule, proofs are ommited. Special attention is paid to some particular density distributions. Sections 6 to 9 deal with two kinds of development in the model - the ``equilibrium mode'' and the ``catastrophic mode''. The former leads to so-called urbanitic laws relating distributions of (population) density to ``rental'' and ``opulence''. In the last section, the Amson's approach is compared to a previous one of the author. The theoretically deduced properties are not compared with any empirical evidence.