Overview

This text presents a unified framework (based on spatial interaction models) that encapsulates most of the models developed so far for the analyses of spatial patterns of human activities at both a static and a dynamic level. It shows how such models can be associated in a static analysis, with macro- and meso-oriented entropy theory and micro-oriented random utility theory. In a dynamic analysis such models can be seen as the result of an optimal trajectory through which a closed system approaches an equilibrium state, in both a deterministic and stochastic framework. However spatial interaction models can exhibit chaotic patterns under particular conditions, since they can be linked to both a logistic form (in a degenerate case) and interrelated logistics (in a general case). Finally, such models may serve to form a broad ""envelope"" incorporating many dynamic models currently used, which end up with logistic structures. The theoretical-methodological foundations are original, as various tools originating from different principles (e.g. economics, mathematics, physics, statistics, biology and natural sciences) are used to develop a unified framework.

Full Product Details

Author:   Professor Peter Nijkamp ,  Aura Reggiani
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Weight:   0.605kg
ISBN:  

9783540554585

ISBN 10:   3540554580
Pages:   278
Publication Date:   12 June 1992
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

A Static Models of Spatial Interaction.- 1. Spatial Interaction Models and Gravity Theory a Concise Overview.- 1.1 Introduction.- 1.2 Gravity Analysis and Spatial Interaction Models.- 1.3 Gravity Theory and the Social Sciences.- 1.4 Alternative Utility Foundations and Specifications of Gravity Theory.- 1.4.1 Simple interaction theory.- 1.4.2 System-wide cost efficiency.- 1.4.3 Aggregate utility theory.- 1.5 The Scope of Gravity Models: Concluding Remarks.- 2. Entropy Theory and Spatial Interaction Analysis.- 2.1 Prologue.- 2.2 Entropy Theory and Spatial Interaction.- 2.3 Alternative Specifications of the Entropy Model.- 2.4 Alternative Theoretical Backgrounds of the Entropy Model.- 2.4.1 An economic utility approach.- 2.4.2 A probabilistic utility approach.- 2.4.3 Statistical information theory.- 2.4.4 Bayesian statistics.- 2.4.5 Maximum likelihood approach.- 2.5 Concluding Remarks.- 3. Entropy and Generalized Cost Minimization Models at the Macro Level.- 3.1 Prologue.- 3.2 Entropy and Linear Programming.- 3.3 Entropy and Geometric Programming.- 3.4 Spatial Patterns of Entropy and Linear Programming Models.- 3.5 Entropy Revisited.- 3.6 Concluding Remarks.- Annex 3A. Relationships Between Total Trip Costs and the Cost Friction Coefficient.- 4. Spatial interaction models and utility maximizing Behaviour at the micro level.- 4.1 Prologue.- 4.2 Spatial Interaction Behaviour and Individual Choice Behaviour: Theory.- 4.2.1 Introduction.- 4.2.2 Spatial interaction models and deterministic utility theory.- 4.2.3 Spatial interaction models and random utility theory.- 4.2.3.1 Basic concepts of random utility theory.- 4.2.3.2 Analogies between spatial interaction models and discrete choice models.- 4.2.4 Concluding remarks.- 4.3 Spatial Interaction Behaviour and Individual Choice Theory: An Application.- 4.3.1 Introduction.- 4.3.2 The model.- 4.3.3 The data.- 4.3.4 Results and concluding remarks.- 4.4 Conclusions.- Annex 4A. An Algorithm for Modal Split Choice with Congestion.- B Dynamic Models of Spatial Interaction.- 5. Dynamic and Stochastic Spatial Interaction Models.- 5.1 Prologue.- 5.2 Spatial Interaction Models Analyzed by Means of Optimal Control.- 5.2.1 Introduction.- 5.2.2 An optimal control approach.- 5.2.3 Concluding remarks.- 5.3 Spatial Interaction Models Analyzed by Means of Stochastic Optimal Control.- 5.3.1 Introduction.- 5.3.2 A stochastic optimal control approach.- 5.3.3 Concluding remarks.- 5.4 Spatial Interaction Models with Catastrophe Behaviour Analyzed in the Framework of Stochastic Optimal Control.- 5.4.1 The model.- 5.4.2 The stochastic optimal control version.- 5.5 Epilogue.- Annex 5A. The Generalized Spatial Interaction Model as a Solution to the Optimal Control Entropy Model.- Annex 5B. A (Generalized) Stochastic Spatial Interaction Model as a Solution to a Stochastic Optimal Control Problem.- Annex 5C. Stability and Bifurcations in a Phase Diagram Analysis for a Stochastic Optimal Control Problem.- 6 Spatial Modelling and Chaos Theory.- 6.1 Prologue.- 6.2 Chaos Theory: A Brief Review.- 6.2.1 A general introduction to non-linear modeling.- 6.2.2 Key issues in the theory of chaos.- 6.3 Spatial Applications of Chaos Theory: A Brief Survey.- 6.3.1 Introduction.- 6.3.2 Dendrinos.- 6.3.3 Dendrinos and Sonis.- 6.3.4 Mosekilde, Aracil and Allen.- 6.3.5 Nijkamp.- 6.3.6 Reiner, Munz, Haag and Weidlich.- 6.3.7 White.- 6.3.8 Zhang.- 6.3.9 Concluding remarks.- 6.4 A Model of Chaos for Spatial Interaction and Urban Dynamics.- 6.4.1 Introduction.- 6.4.2 Results of simulation experiments.- 6.4.2.1 The onset of chaotic motion.- 6.4.2.2 Chaotic urban evolution.- 6.4.3 Concluding remarks.- 6.5 Epilogue.- Annex 6A. Classification of Two-dimensional Critical Points.- Annex 6B. Strange Attractors: A Brief Overview.- Annex 6C. Steady State Solutions for a Generalized Lorenz System.- 7. Spatial Interaction Models and Chaos Theory.- 7.1 Prologue.- 7.2 Chaos in Spatial Interaction Models.- 7.2.1 Introduction.- 7.2.2 Chaotic elements in dynamic logit model: theory.- 7.2.3 Simulation experiments for a dynamic logit model.- 7.2.3.1 Dynamic processes in logit models.- 7.2.3.2 Dynamic processes in spatial interaction models.- 7.2.4 Concluding remarks.- 7.3 Delay Effects in Dynamic (Binary) Logit Models.- 7.3.1 Introduction.- 7.3.2 A logistic model with multiple delays.- 7.3.3 Concluding remarks.- 7.4 Conclusions.- Annex 7A. Stability Solutions for a Dynamic Logit Model.- Annex 7B. Stability Solutions for a Dynamic Spatial Interaction Model.- 8. Spatial Interaction Analysis and Ecologically-Based Models.- 8.1 Prologue.- 8.2 Prey-Predator Models: Introduction.- 8.3 Synergetic Models of Spatial Interaction.- 8.4 An Optimal Control Model for a Spatial Prey-Predator System.- 8.4.1 Introduction.- 8.4.2 Equilibrium analysis.- 8.4.3 Concluding remarks.- 8.5 Competition Models: Introduction.- 8.6 Impact of Chaotic Evolution in Spatial Competition.- 8.6.1 Introduction.- 8.6.2 The case of two competing regions.- 8.6.2.1 Equilibrium analysis.- 8.6.2.2 Simulation experiments.- 8.6.3 Concluding remarks.- 8.7 Epilogue.- Annex 8A. Stability Solutions for an Optimal Control Prey-Predator Problem.- Annex 8B. Transformation of a Continuous System into a Discrete System.- Annex 8C. Stability Analysis for a Particular Competing System.- 9. Retrospect and Prospect.- 9.1 Retrospect.- 9.2 Typology of Dynamic Spatial Interaction Models.- 9.2.1 Introduction.- 9.2.2 Macro-dynamic approaches.- 9.2.3 Micro-meso dynamic approaches.- 9.3 Evolution of Spatial Interaction Models.- 9.4 New Research Areas.- References.

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