Dynamics of generalised spatial interaction models

Abstract This paper analyses dynamic properties of generalised spatial interaction models, with particular emphasis on Alonso's general theory of movements. Although the application of this theory addressed in the paper is a multiregional demographic stock–flow model, the approach can also be adopted to other types of spatial interaction phenomena. Equilibrium and stability conditions are examined by rewriting the generalised spatial interaction model as a general non-linear dynamic Volterra–Lotka model. More insight into local and global stability is obtained by means of simulation experiments which identify a variety of stable and unstable time trajectories.

[1]  Dave Giles,et al.  Growth centres, city size, and urban migration in New Zealand , 1976 .

[2]  Luc Anselin,et al.  SPECIFICATION TESTS AND MODEL SELECTION FOR AGGREGATE SPATIAL INTERACTION: AN EMPIRICAL COMPARISON* , 1984 .

[3]  Peter F. Colwell,et al.  CENTRAL PLACE THEORY AND THE SIMPLE ECONOMIC FOUNDATIONS OF THE GRAVITY MODEL , 1982 .

[4]  G. Leonardi,et al.  An Optimal Control Representation of a Stochastic Multistage-Multiactor Choice Process , 1983 .

[5]  T. Suruga,et al.  Migration, age, and education: a cross-sectional analysis of geographic labor mobility in Japan. , 1981, Journal of regional science.

[6]  J. Ledent,et al.  On the Relationship between Alonso's Theory of Movement and Wilson's Family of Spatial-Interaction Models , 1981 .

[7]  Spatial externalities and the stability of interacting populations near the center of a large area. , 1982, Journal of regional science.

[8]  P. Langley.  The Spatial Allocation of Migrants in England and Wales: 1961-66 , 1974 .

[9]  Peter Nijkamp,et al.  Reflections On Gravity and Entropy Models , 1975 .

[10]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[11]  Andrei Rogers,et al.  Introduction to Multistate Mathematical Demography , 1980 .

[12]  R M May,et al.  Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos , 1974, Science.

[13]  D. Dendrinos.  ON THE DYNAMIC STABILITY OF INTERURBAN/REGIONAL LABOR AND CAPITAL MOVEMENTS* , 1982 .

[14]  J. H. Niedercorn,et al.  AN ECONOMIC DERIVATION OF THE “GRAVITY LAW” OF SPATIAL INTERACTION* , 1969 .

[15]  Chang-i Hua,et al.  An econometric procedure for estimation of a generalized systemic gravity model under incomplete information about the system , 1981 .

[16]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[17]  Jacques Poot,et al.  A SYSTEM APPROACH TO MODELLING THE INTER‐URBAN EXCHANGE OF WORKERS IN NEW ZEALAND* , 1986 .

[18]  A. C. Mead.  A simultaneous equations model of migration and economic change in nonmetropolitan areas. , 1982, Journal of regional science.

[19]  M. Greenwood,et al.  An Analysis of the Determinants of Geographic Labor Mobility in the United States , 1969 .

[20]  J. Vanderkamp,et al.  Migration Flows, Their Determinants and the Effects of Return Migration , 1971, Journal of Political Economy.

[21]  P. Nijkamp,et al.  Spatial Choice and Interaction Models: Criteria and Aggregation , 1980 .

[22]  Chang-i Hua,et al.  An Exploration of the Nature and Rationale of a Systemic Model , 1980 .

[23]  M. Greenwood,et al.  Migration and Economic Growth in the United States. , 1982 .

[24]  Lawrence A. Brown,et al.  On the Use of Markov Chains in Movement Research , 1970 .

[25]  G. Hardin.  The competitive exclusion principle. , 1960, Science.

[26]  L. Anselin.  Implicit functional relationships between systematic effects in a general model of movement , 1982 .

[27]  E. Casetti.  A CATASTROPHE MODEL OF REGIONAL DYNAMICS , 1981 .

[28]  F. Porell,et al.  Intermetropolitan migration and quality of life. , 1982, Journal of regional science.

[29]  Andrei Rogers.  Matrix Analysis of Interregional Population Growth and Distribution , 1968 .

[30]  P. Langley.  Inter-regional migration and economic opportunity, Australia, 1966-71. , 1977, The Economic record.

[31]  J. Ledent,et al.  Modeling the Dynamics of a System of Metropolitan Areas: A Demoeconomic Approach , 1980, Environment & planning A.

[32]  T. Tabuchi.  The systemic variables and elasticities in Alonso's general, theory of movement , 1984 .

[33]  J. Ledent.  Calibrating Alonso's General Theory of Movement: the Case of Inter-Provincial Migration Flows in Canada , 1980 .

[34]  Alan Wilson,et al.  A Family of Spatial Interaction Models, and Associated Developments , 1971 .

[35]  O. Fisch.  Contributions to the general theory of movement , 1981 .