Chaos and Socio-Spatial Dynamics

ISBN-13: 9780387972831 / Angielski / Twarda / 1990 / 184 str.

Dimitrios S. Dendrinos

Opis

Presents a discrete in time-space universal map of relative dynamics that is used to unfold an extensive catalogue of dynamic events not previously discussed in mathematical or social science literature.

Spis treści

Prologue.- I. Socio-Spatial Dynamics.- A. Introduction.- 1. A Brief Look at the Literature.- 2. Some Simple Dynamic Models.- 3. The Location-Dependent Elements of a Theory of Socio-Spatial Dynamics.- B. The Four Lenses to View Socio-Spatial Dynamics.- 1. The Absolute-Relative Lens.- 2. Continuous Dynamics.- 3. Discrete Dynamics: The Universal Discrete Relative Dynamics Model.- Conclusions.- II. One Stock, Two Regions.- Summary.- A. The First Iterate and Associated Analytical Properties of the Model: x(t + 1) = 1/1 + AF[x(t)].- 1. Overview.- 2. Fixed-Point Behavior and the Discrete Map.- 3. Competitive Exclusion Equilibria.- 4. Classification of Fundamental Relative Spatial Dynamics.- B. Log-Linear Comparative Advantages Producing Functions: F = x(t)a[l – x(t)]b.- 1. Interpretation and Discussion of the Log-Linear Model.- 2. Intervals of Stability of Equilibria.- 3. Analytical Properties of the Log-Linear Model.- 4. Geometric Description of the Iterative Process.- C. Higher Iterates and Fundamental Bifurcations in Discrete Dynamics.- 1. The Second Iterate and Two-Period Cycles.- 2. Analytical Description of Two-Period Cycles.- 3. Period-Doubling and the Feigenbaum Slope-Sequences.- 4. Domains of Nonexistence of k-Period Cycles (k ? 3) and the Hopf Equivalent Bifurcation.- D. The Exponential Locational Advantages Producing Function.- Conclusions.- III. One Stock, Multiple Locations.- Summary.- A. The General Model.- 1. Analytical Results.- 2. Ranking of Stocks According to Size.- 3. Trajectory Domains for the One-Stock, Three-Location Model.- B. The Log-Linear Comparative Advantages Model.- 1. Analytical Properties.- 2. Numerical Analysis for the One-Stock, Multiple-Location Model.- C. Empirical Evidence.- 1. The Nine U.S. Regions and Their Aggregations.- 2. The Time Step and the Forces at Work.- 3. U.S. Regional Relative Population Instability.- 4. The Statistical Tests of Significance.- D. Border Sequences in the One-Stock, Multiple-Location, Log-Linear Model.- 1. Some General Results.- 2. Areas of State Variable Movement in the One-Stock, Three-Location, Log-Linear Model.- E. One-Stock, Multiple-Location, Discrete-Time, Logistic Growth.- 1. Definition and Central Analytical Properties.- 2. The Jacobi Matrix.- 3. Equilibria.- Conclusions.- IV. Multiple Stocks, Multiple Locations.- Summary.- A. The General Model.- 1. Analytical Results.- 2. The Log-Linear Specification.- B. The Two-Stock, Two-Location Model.- 1. The General Case.- 2. The Log-Linear Specifications.- 3. An Example.- 4. Numerical Results for the Two-Stock, Two-Location, Log-Linear Model.- C. The Two-Stock, I-Location Case.- 1. The General Specifications.- 2. The Log-Linear Specifications.- D. The Two-Stock, Multiple-Location, Discrete-Time, Logistic Growth Model.- 1. Definitions and Analytical Properties.- 2. The Jacobi Block-Matrix.- 3. Dynamic Structure of the Equilibria.- Conclusions.- Epilogue.- 1. Six Central Issues.- 2. Three Areas of Application.- 3. Further Research Suggestions.- Appendix I Second-Order Determinants of the Three-Location, One-Stock Model.- Appendix II The Determinant of the Log-Linear Model.- References.- Author Index.