The task of combining evolutionary migration models with stochastic utility theory is undertaken in a series of three interrelated papers. The present, first, paper deals with the evolution of migratory systems and its dynamics are drawn mainly from work by Haag and Weidlich. A migratory system is defined and then the foundations upon which the evolution of such a system is based are described, including an approximation due to Kurtz which allows the most probable state of the evolutionary model to be represented as a dynamical system. This paper closes with a discussion of disequilibrium, which is central in this series. Disequilibrium is related to the concept of a steady state, the existence of which is established for nonlinear migratory systems of the type discussed here.
Get full access to this article
View all access options for this article.
References
1.
BattyM, 1978, “Operational urban models incorporating dynamics in a static framework” in Spatial Interaction Theory and Planning Models Eds KarlqvistALundqvistLSnickarsFWeibullJ W, (North-Holland, Amsterdam) pp 222–252.
2.
Ben-AkivaM, 1973Structure of Passenger Travel Demand ModelsPhD thesis, Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139.
3.
Ben-AkivaMLermanS R, 1985Discrete Choice Analysis: Theory and Application to Travel Demand (MIT Press, Cambridge, MA).
4.
de PalmaA MBen-AkivaM, 1981, “An interactive dynamic model of residential location choice”paper presented at the international conference on Structural Economic Analyses and Planning in Time and Space, Umeä, Sweden; copy available from the first author, Department of Economics, Queen's University, Kingston, Ontario K7L 3N6.
5.
de PalmaALefévreC, 1983, “Individual decision-making in dynamic collective systems”Journal of Mathematical Sociology90103–124.
6.
DomencichTMcFaddenD, 1975Urban Travel Demand: A Behavioural Analysis (North-Holland, Amsterdam).
7.
FeeneyG, 1973, “Two models for multiregional population dynamics”Environment and Planning531–43.
8.
GrunbergFModiglianiF, 1954, “The predictability of social events”Journal of Political Economy62456–478.
9.
HaagGWeidlichW, 1984, “A stochastic theory of interregional migration”Geographical Analysis16331–357.
10.
HakenH, 1977Synergetics, an Introduction (Springer, Berlin).
11.
HararyFLipsteinBStyanG, 1970, “A matrix approach to non-stationary chains”Operations Research181168–1181.
12.
HearonJ Z, 1963, “Theorems on linear systems”Annals of the New York Academy of Sciences10836–66.
13.
KurtzT G, 1978, “Strong approximation theorems for density-dependent Markov chains”Stochastic Processes and Their Applications6223–240.
14.
LiawK-LBartelsCPA, 1982, “Estimation and interpretation of a non-linear migration model”Geographical Analysis14227–245.
15.
McFaddenD, 1974, “Conditional logit analysis of qualitative choice behavior” in Frontiers in Econometrics Ed. ZarembkaP, (Academic Press, New York) pp 105–142.
16.
McFaddenD, 1978, “Modelling the choice of residential location” in Spatial Interaction Theory and Planning Models Eds KarlqvistALundqvistLSnickarsFWeibullJ W, (North-Holland, Amsterdam).
17.
MossW G, 1979, “A note on individual choice models of migration”Regional Science and Urban Economics91–11.
18.
NicolisGPrigogineI, 1977Self-organization in Non-equilibrium Systems (John Wiley, New York).
19.
PicklesA, 1980, “Models of movement: A review of alternative methods”Environment and Planning A121383–1404.
20.
PowellM J D, 1970, “A FORTRAN subroutine for solving systems of non-linear algebraic equations” in Numerical Methods for Non-linear Algebraic Equations Ed. RabinowitzP, (Gordon and Breach, London).
21.
RavensteinE, 1885, “The laws of migration”Journal of the Royal Statistical Society48167–227.
22.
RogersA, 1967, “Matrix analysis of interregional population growth and distribution”Papers of the Regional Science Association18177–196.
23.
SmithT E, 1975, “A choice theory of spatial interaction”Regional Science and Urban Economics5137–176.
ViningD RJr, 1975, “The spatial distribution of human populations and its characteristic evolution over time: Some recent evidence from Japan”Papers of the Regional Science Association35157–178.
26.
WeidlichWHaagG, 1983Concepts and Models of a Quantitative Sociology (Springer, Berlin).
27.
WeinbergD H, 1975Intra-urban Household MobilityPhD thesis, Department of Sociology, Yale University, New Haven, CT 06520.
28.
WilsonA G, 1970Entropy in Urban and Regional Modelling (Pion, London).
