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POPULATION DENSITY FUNCTIONS: A DIFFERENTIAL EQUATION APPROACH *
Author(s) -
Nairn Alasdair G. M.,
O'Neill Gerard J.
Publication year - 1988
Publication title -
journal of regional science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.171
H-Index - 79
eISSN - 1467-9787
pISSN - 0022-4146
DOI - 10.1111/j.1467-9787.1988.tb01198.x
Subject(s) - mathematics , differential equation , population , differential (mechanical device) , metropolitan area , probability density function , mathematical analysis , statistics , physics , geography , demography , archaeology , sociology , thermodynamics
This paper introduces a new mathematical technique to describe population density functions. Two length scales, which characterize the variation of these density functions within a region, are identified. A differential equation is derived and asymptotic solutions obtained. Two specific techniques, the method of matched asymptotic expansions and the method of multiple scales, are introduced and illustrated by application to population densities at both the metropolitan and regional levels.