Synopsis
I Formal Models in Economics.- 1 A chaotic process with slow feed back: The case of business cycles.- 1.1 A first model.- 1.1.1 Investments.- 1.1.2 Consumption.- 1.2 The cubic iterative map.- 1.2.1 Fixed points, cycles and chaos.- 1.2.2 Formal analysis of chaotic dynamics.- 1.2.3 Symbolic dynamics.- 1.3 "Brownian random walk".- 1.4 Digression on order and disorder.- 1.5 The general model.- 1.5.1 Relaxation cycles.- 1.5.2 Other cycles.- 1.5.3 The Slow Feed Back.- 1.6 Conclusion.- 2 Nonlinear Interactions in the Economy.- 2.1 Introduction.- 2.2 The Long Wave Model.- 2.3 Mode-Locking and Chaos.- 2.4 Conclusion.- 3 Fast and Slow Processes of Economic Evolution.- 3.1 Introduction and Background.- 3.2 The Problems of Economic Development Theory.- 3.3 Synergetic Development Economics - Some Basic Concepts.- 3.4 The Arena.- 3.5 Rules of the Game.- 3.6 Networks.- 3.7 Knowledge As Networks and Knowledge On Networks.- 3.8 Communication and Creativity - some Historical Evidence.- 3.9 Creativity and Communications - Econometric Results.- 3.10 The Inverted Explanation.- 3.11 The Destruction of the Industrial Society.- 3.12 The New Economic Structure.- 4 A stochastic model of technological evolution.- 4.1 Introduction.- 4.2 A Substitution Model.- 4.3 Application of a general evolutionary model to technological change.- 4.4 Discussion.- 5 Evolution of Production Processes.- 5.1 Introduction.- 5.2 Basic Assumptions.- 5.3 Formalization.- 5.4 Chernenko's Results.- 5.5 An alternative macro model.- 5.6 Simulation results.- 5.7 Modeling evolution on the individual level.- 5.7.1 Simulation run with total extinction.- 5.7.2 Simulation run without extinction.- 5.8 Conclusions.- 6 Innovation Diffusion through Schumpeterian Competition.- 6.1 Introduction: From "Homo Economicus" to "Homo Socialis": Innovation diffusion as a collective socio-ecological dynamic choice process.- 6.2 Analytical basis of Schumpeterian Competition: Collective choice and relative socio-spatial dynamics.- 6.3 Explicit analytical presentation of the innovation diffusion dynamics: Dynamic choice models.- 6.4 Intervention of an active environment: Generation of innovation adoption niches.- 6.5 Temporal innovation diffusion process.- 6.5.1 Qualitative analysis of the Schumpeter competition cycles for Clusters of competitive innovations.- 6.5.2 Variational principle of meso-level collective choice behaviour.- 6.6 Concluding Remark.- 7 Nonlinear Threshold Dynamics: Further Examples for Chaos in Social Sciences.- 7.1 Introduction.- 7.2 A Short Course into Chaos.- 7.3 How Addictive Behaviour and Threshold Adjustment May Imply Chaos.- 7.4 How Asymmetric Investment Behaviour of Two Competing Firms Generates Chaos.- 7.5 Concluding Remarks.- II Formal Models in Geography.- 8 Geography Physics and Synergetics.- 8.1 Introduction.- 8.2 Models of geographical interactions.- 8.2.1 Polarization and gravitation.- 8.2.2 Reformulations of the gravity model.- 8.2.3 The entropy maximizing approach.- 8.2.4 About men and particles.- 8.3 Models of geographical structures.- 8.3.1 The relativity of geographical space.- 8.3.2 Fractality of geographical space.- 8.3.3 Space-time convergence.- 8.3.4 The example of urban hierarchies.- 8.3.5 Processes and geographical forms.- 8.4 Conclusion.- 9 Chaotic Behaviour in Spatial Systems and Forecasting.- 9.1 Introduction.- 9.2 An Example for Chaotic Evolution: Migratory Systems.- 9.2.1 A Numerical Simulation.- 9.3 Estimation of Trend Parameters.- 9.4 The Estimation Procedure.- 9.5 Forecasting for Systems with Chaotic Evolution.- 9.5.1 Step I: Confidence Limits on Model Parameters by Monte Carlo Estimation.- 9.5.2 Step II: Monte Carlo Simulation of Systems Trajectories.- 10 Model Identification for Estimating Missing Values in Space-Time Data Series: Monthly Inflation in the US Urban System, 1977-1990.- 10.1 Introduction.- 10.2 Background.- 10.3 Update of individual urban area ARIMA models.- 10.4 Jackknife results for New York and Los Angeles.- 10.5 Transfer function
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