Nonlinear discrete relative population dynamics of the U.S. regions

doi:10.1016/0096-3003(88)90124-5

Applied Mathematics and Computation

Volume 25, Issue 4, March 1988, Pages 265-285

https://doi.org/10.1016/0096-3003(88)90124-5 Get rights and content

Abstract

A new discrete relative-dynamics algorithm is tested using population interactions of U.S. regions. A 133-year time period is used (1850–1983) to calibrate the log-linear model's parameters using standard linear regression tests. We also report certain forecasts under different spatial disaggregation schemes of the U.S. regions, and under two different time-period steps (iterations) to the year 2050. All forecasts imply competitive exclusion for the northern regions; under certain areal disaggregations and time (iteration) steps the southern or western region also experiences conditions leading to drastic declines in their share of the U.S. population. We also report the results of certain random fluctuations on the model's parameters and their implications regarding the dynamics of the U.S. regional population structure. The outcomes seem to be robust under these fluctuations.

References (15)

D.S. Dendrinos et al.
The onset of turbulence in discrete relative multiple spatial dynamics
J. App. Math. Comp.
(1987)
D.S. Dendrinos, Turbulence and fundamental urban/regional dynamics, presented at the Annual Meeting of the American...
D.S. Dendrinos
Regions, antiregions and their dynamic stability: The case of the U.S. (1929–79)
J. Regional Sci.
(1984)
D.S. Dendrinos
Ecological Studies of Urban Nonlinear Dynamics
D.S. Dendrinos et al.
Urban Evolution: Studies in the Mathematical Ecology of Cities
(1985)
D.S. Dendrinos et al.
Turbulence and Socio-Spatial Dynamics: Toward a Structural Theory of Social Systems Evolution
(1988)
M.J. Feigenbaum
Quantitative universality for a class of non-linear transformations
J. Statist. Phys.
(1978)

There are more references available in the full text version of this article.

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^☆: Part of this research was done under contract number SES-82-16620 with the National Science Foundation, which is gratefully acknowledged, by D.S. Dendrinos.

^†: This author wishes to thank his research assistant Medrdad Givenchi for the computer work.

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Nonlinear discrete relative population dynamics of the U.S. regions☆

Abstract

J. App. Math. Comp.

Regions, antiregions and their dynamic stability: The case of the U.S. (1929–79)

J. Regional Sci.

Ecological Studies of Urban Nonlinear Dynamics

Urban Evolution: Studies in the Mathematical Ecology of Cities

Turbulence and Socio-Spatial Dynamics: Toward a Structural Theory of Social Systems Evolution

Quantitative universality for a class of non-linear transformations

J. Statist. Phys.