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Towards a Science of Complexity in Spatial-Economic Systems

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Recent Advances in Spatial Equilibrium Modelling

Part of the book series: Advances in Spatial Science ((ADVSPATIAL))

Abstract

Conventional (spatial) economic equilibrium models have usually taken for granted the existence of well-behaved functional forms of state equations, so that existence conditions for optimal solutions could in principle be established. Irregular behaviour was an exception in the tradition of equilibrium analysis. Recent years have witnessed among economists an increasing popularity of nonlinear dynamic models. The wide range of theories and reflections on evolutionary dynamic systems reflects the continuously rising interest of economists in ‘economics without equilibrium’ (Kaldor 1985). Kaldor notes in the Okun Memorial Lectures: “it seems clear that if we are to get out of the present impasse we must begin by constructing a different kind of abstract model, one that recognizes from the beginning that time is a continuing and irreversible process; that it is impossible to assume the constancy of anything over time, such as the supply of labour or capital, the psychological preferences for commodities, the nature and number of commodities, or technical knowledge” (Kaldor 1985 p 61).

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References

  • Allen RGD (1959) Mathematical Economics. MacMillan, London (2nd edition)

    Google Scholar 

  • Andersson ÄE, Batten DF (1988) Creative Nodes. Logistical Networks and the Future of the Metropolis. Transportation 14: 281–293

    Google Scholar 

  • Baker GL, Gollub JP (1990) Chaotic Dynamics. An Introduction. Cambridge University Press, Cambridge

    Google Scholar 

  • Batten D, Casti J, Johansson B (Eds) (1987) Economic Evolution and Structural Adjustment. Springer-Verlag, Berlin

    Google Scholar 

  • Batty M, Longley PA (1986) The Fractal Simulation of Urban Structure. Environment and Planning A 18: 1143–1179

    Article  Google Scholar 

  • Brock WA (1986) Distinguishing Random and Deterministic Systems. Abridged Version. Journal of Economic Theory 40: 168–195

    Article  Google Scholar 

  • Common M, Perrings C (1992) Towards on Ecological Economics of Sustainability. Ecological Economics 6: 7–34

    Article  Google Scholar 

  • Crilly T (1991) The Roots of Chaos. A Brief Guide. Fractals and Chaos. Crilly AJ, Earnshaw RA, Jones H (Eds). Springer-Verlag, Berlin, pp 193–209

    Chapter  Google Scholar 

  • Davies PCW (1989) The Physics of Complex Organization. Theoretical Biology. Epigenetic and Evolutionary Order from Complex Systems. Goodwin B, Saunders P ( Eds) Edinburgh University Press, Edinburgh pp 101–111

    Google Scholar 

  • Day RH (1985) Dynamical Systems Theory and Complicated Economic Behaviour. Environment and Planning B 2: 55–64

    Google Scholar 

  • Dendrinos DS, Mullally H (1985) Urban Evolution. Studies in the Mathematical Ecology of Cities. Oxford University Press, Oxford

    Google Scholar 

  • Diappi L, Reggiani A (1996) Evolutionary Models in Spatial Systems. Qualitative vs Quantitative Approaches. Ten Years of Regional Science. Camagni R, Senn L (Eds )

    Google Scholar 

  • Franco Angeli, Milano (forthcoming) Eckalbar JA (1992) Book Review of ‘From Catastrophe to Chaos’ by JB Rosser. Journal of Economic Literature 30: 2150–2151

    Google Scholar 

  • Eckmann JP, Ruelle D (1985) Ergodic Theory of Chaos and Strange Attractors. Review of Modern Physics 57: 617–656

    Article  Google Scholar 

  • Feigenbaum HJ (1978) Quantitative Universitality for a Class of Non-Linear Transformations. Journal of Statistical Planning 19: 25–52

    Article  Google Scholar 

  • Fischer MM, Nijkamp P, Papageorgiou YY (1990) Spatial Choices and Processes. North-Holland, Amsterdam

    Google Scholar 

  • Forrester J (1968) Principles of Systems. Wright-Allen, Press, Cambridge, Mass.

    Google Scholar 

  • Frank M, Stengos T (1988) Chaotic Dynamics in Economic Time-Series. Journal of Economic Surveys 2: 103–133

    Article  Google Scholar 

  • Frankhauser P (1991) Aspects Fractals des Structures Urbaines. L’Espace Géographique 1: 45–69

    Google Scholar 

  • Frisch R (1933) Propagations Problems and Impulse Problems in Dynamic Economics. Economic Essays in Honour of Gustav Cassel. Allen & Unwin, London

    Google Scholar 

  • Georgescu-Roegen (1974) Dynamic Models and Economic Growth. Economic Appliquée 27: 529–563

    Google Scholar 

  • Grandmont J-M (1991) Expectations Driven Business Cycles. European Economic Review 35: 293–299

    Article  Google Scholar 

  • Greiner A, Kugler F (1994) A Note on Competition Among Techniques in the Presence of Increasing Returns of Scale. Evolutionary Economics and Chaos Theory. Leydesdorff L, Besselaar P van den ( Eds) Pinter, London, pp 44–52

    Google Scholar 

  • Guckenheimer J (1979) Sensitive Dependence to Initial Condions for One-Dimensional Maps. Communications in Mathematical Physics 70: 133–160

    Article  Google Scholar 

  • Haken H (1983a) Synergetics. Springer-Verlag, Berlin

    Google Scholar 

  • Haken H (1983b) Advanced Synergetics. Springer-Verlag, Berlin

    Google Scholar 

  • Hao B-L (Ed) (1984) Chaos. World Scientific Publication Co, Singapore

    Google Scholar 

  • Hirsh M, Smale S (1974) Differential Equations, Dynamical Systems and Linear Algebra. Academic Press, London

    Google Scholar 

  • Holden AV, Muhamad MA (1986) A Graphical Zoo of Strange and Peculiar Attractors. Chaos. Holden AV ( Ed) Manchester University Press, Manchester pp 15–35

    Google Scholar 

  • Hommes CH (1991) Chaotic Dynamics in Economic Models. Wolters-Noordhoff, Groningen

    Google Scholar 

  • Kaldor N (1985) Economics Without Equilibrium. University College Cardiff Press, Cardiff

    Google Scholar 

  • Kapur JN, Kumar U, Kumar V. (1992) Some Possible Models for Technological Innovation Diffusion. Journal of Scientific and Industrial Research 51: 202–208

    Google Scholar 

  • Kélsey D (1988) The Economics of Chaos or the Chaos of the Economics. Oxford Economic Papers 40: 1–3

    Google Scholar 

  • Leydesdorff L, Besselaar P van den ( Eds ) (1994) Evolutionary Economics and Chaos Theory. Pinter, London

    Google Scholar 

  • Leydesdorff L (1994) New Models of Technological Change. New Theories for Technology Studies? Evolutionary Economics and Chaos Theory. Leydesdorff L, Besselaar P van den, ( Eds) Pinter, London pp 181–192

    Google Scholar 

  • Levins R (1968) Evolution in Changing Environments. Some Theoretical Explorations. Princeton University Press, Princeton

    Google Scholar 

  • Li TY, Yorke JA (1975) Period Three Implies Chaos. American Mathematical Monthly 82: 985–992

    Article  Google Scholar 

  • Lichtenberg AJ, Lieberman MA (1983) Regular and Stochastic Motion. Springer-Verlag, Berlin

    Google Scholar 

  • Longley P, Batty M (1994) Fractal Cities. Academic Press, London

    Google Scholar 

  • Lorenz EN (1963) Deterministic Non-Periodic Flow. Journal of the Atmospheric Sciences 20: 130–141

    Article  Google Scholar 

  • Lorenz H-W (1989) Non-Linear Dynamical Economics and Chaotic Motion. Lecture Notes in Economics and Mathematical System 334. Springer-Verlag, Berlin

    Google Scholar 

  • Maggioni MA (1993) Ecological Dynamics and Critical Mass in the Location of High-Tech Firms. Paper presented at the 40th North American RSAI Conference. Houston, TX

    Google Scholar 

  • Mahajan V, Muller E, Bass FM (1990) New Product Diffusion Models in Marketing. A Review and Directions for Research. Journal of Marketing 54: 1–21

    Article  Google Scholar 

  • Mandelbrot B (1977) The Fractal Geometry of Nature. VH Dreeman and Company, New York

    Google Scholar 

  • Manneville P, Pomeau Y (1979) Intermittency and the Lorenz Model. Physics Letters A 75: 1–2

    Article  Google Scholar 

  • Marsden JE, McCracken M (1976) The Hopf Bifurcation and its Applications. Springer-Verlag, Berlin

    Book  Google Scholar 

  • May RM (1976) Simple Mathematical Models with Very Complicated Dynamics. Nature 261: 459–467

    Article  Google Scholar 

  • Meadows DL, Meadows DH (Eds) (1973) Toward Global Equilibrium. Collected Papers. Wright-Allen Press, Cambridge, Mass.

    Google Scholar 

  • Medio A (1979) Teoria Non Lineare del Ciclo Economico. I I Mulino, Bologna

    Google Scholar 

  • Medio A (1989) Discrete and Continuous Models of Chaotic Dynamics in Economics. Department of Economics, University of Venice

    Google Scholar 

  • Mees A (1975) The Revival of Cities in Mediaeval Europe. An Application of Catastrophe Theory. Regional Science and Urban Economics 5: 403–425

    Article  Google Scholar 

  • Morishima M (1991) General Equilibrium Theory in the Twenty-First Century. The Economic Journal 101: 69–74

    Article  Google Scholar 

  • Newhouse S, Ruelle D, Takens F (1978) Occurrence of Strange Axiom-A Attractors near Quasiperiodic Flow or Tm, m 3. Communications in Mathematical Physics 64: 35–40

    Article  Google Scholar 

  • Nijkamp P (1987) Long Term Economic Fluctuations. A Spatial View. Socio-Economic Planning Sciences 21: 189–197

    Article  Google Scholar 

  • Nijkamp P, Reggiani A (1990) An Evolutionary Approach to the Analysis of Dynamic Systems with Special Reference to Spatial Interaction Models. Sistemi Urbani 1: 601–614

    Google Scholar 

  • Nijkamp P, Reggiani A (1992a) Interaction, Evolution and Chaos in Space. Springer-Verlag, Berlin

    Chapter  Google Scholar 

  • Nijkamp P, Reggiani A (1992b) Spatial Competition and Ecologically Based Socio-Economic Models. Socio-Spatial Dynamics 3

    Google Scholar 

  • Nijkamp P, Reggiani A (Eds) (1993) Nonlinear Evolution of Spatial Economic Systems. Springer-Verlag, Berlin

    Google Scholar 

  • Nijkamp P, Reggiani A (1995) Nonlinear Evolution of Dynamic Spatial Systems. The Relevance of Chaos Theory and Ecologically Based Models. Regional Science and Urban Economics 25: 183–210

    Article  Google Scholar 

  • Nijkamp P, Reggiani A (1996) Space Time Synergetics in Innovation Diffusion. A Nested Network Simulation Approach. Geographical Analysis (forthcoming)

    Google Scholar 

  • Nusse HE (1987) Asymptotically Periodic Behaviour in the Dynamics of Chaotic Mapping. SIAM Journal of Applied Mathematics 47: 498–515

    Article  Google Scholar 

  • Okun AM (1981) Prices and Quantities. Basil Blackwell, New York

    Google Scholar 

  • Peitgen HO, Richter PH (1986) The Beauty of Fractals. Springer-Verlag, Berlin

    Book  Google Scholar 

  • Perrings C (1994) Ecological Resilience in the Sustainability of Economic Development. Proceedings International Symposium on Models of Sustainable Development. AFCET, Paris pp 27–41

    Google Scholar 

  • Peters T (1988) Thriving on Chaos. MacMillan, London

    Google Scholar 

  • Poincaré H (1913) The Foundation of Science. Science and Method. (English Translation: The Science Press, Lancaster, 1946 )

    Google Scholar 

  • Poston T, Stewart I (1978) Catastrophe Theory and its Applications. Pitman, London

    Google Scholar 

  • Prigogine I (1976) Order through Fluctuation. Self-Organization and Social System. Evolution and Consciousness. Jantsch E, Waddington CH (Eds) Addison-Wesley, Reading, Mass

    Google Scholar 

  • Puu T (1989) Non-Linear Economic Dynamics. Springer-Verlag, Berlin

    Google Scholar 

  • Reggiani A, Nijkamp P (1994) Evolutionary Dynamics in Technological Systems. A Multi-layer Niche Approach. Evolutionary Economics and Chaos Theory. Leydesdorff L, Besselaar P van den ( Eds) Pinter, London pp 93–108

    Google Scholar 

  • Reggiani A, Nijkamp P (1995a) Competition and Complexity in Spatially Connected Networks. Analysis and Simulation. Systems Dynamics Review 11: 51–66

    Article  Google Scholar 

  • Reggiani A, Nijkamp P (1995b) Multilayer Networks and Dynamics Transport Systems. Geographical Systems 2: 39–57

    Google Scholar 

  • Rosser JB (1991) From Catastrophe to Chaos: A General Theory of Economic Discontinuities. Kluwer, Dordrecht

    Book  Google Scholar 

  • Ruelle D, Takens F (1971) On the Nature of Turbulence. Communications in Mathematical Physics 20: 167–192

    Article  Google Scholar 

  • Samuelson PA (1947) Foundations of Economic Analysis. Harvard University Press, Cambridge, Mass.

    Google Scholar 

  • Schuster HG (1988) Deterministic Chaos. VCH, Weinheim Sparrow C (1980) Bifurcation and Chaotic Behaviour in Simple Feedback Systems. Journal of Theoretical Biology 83: 93–105

    Google Scholar 

  • Turner J (1980) Non Equilibrium Thermodynamics, Dissipative Structures and Self-Organization. Dissipative Structures and Spatio-Temporal Organization Studies in Biomedical Research. Scott G, MacMillan J ( Eds) Iowa State University Press, Iowa pp 13–52

    Google Scholar 

  • Thorn R (1975) Structural Stability and Morphogenesis. Addison-Wesley, Reading

    Google Scholar 

  • Thorn R (1989) An Inventory of Waddingtonian Concepts. Theoretical Biology. Goodwin B, Saunders P ( Eds) Edinburgh University Press, Edinburgh pp 1–7

    Google Scholar 

  • Vivien (1994) Bioeconomics and Sustainable Development. Proceedings International Symposium on Models of Sustainable Development. AFCET, Paris pp 875–886

    Google Scholar 

  • Wilson AG (1981) Catastrophe Theory and Bifurcation. Croom Helm, London

    Google Scholar 

  • Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Determining Lyapunov Exponents from a Time Series. Physica D 16: 285–317

    Article  Google Scholar 

  • Zeeman EC (1977) Catastrophe Theory. Selected Papers 1972–1977. Addison-Wesley, Reading

    Google Scholar 

  • Zhang WB (1990) Economic Dynamics. Springer-Verlag, Berlin

    Google Scholar 

  • Zhang WB (1991) Synergetic Economics. Springer-Verlag, Berlin

    Book  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Bologna, Italy

    Aura Reggiani

  2. Vrije Universiteit, Netherlands

    Peter Nijkamp

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  1. Aura Reggiani
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  2. Peter Nijkamp
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Editors and Affiliations

  1. Faculty of Economics Department of Spatial Economics, Free University, De Boelelaan 1105, NL-1081 HV, Amsterdam, The Netherlands

    Jeroen C. J. M. van den Bergh , Peter Nijkamp  & Piet Rietveld ,  & 

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© 1996 Springer-Verlag Berlin · Heidelberg

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Reggiani, A., Nijkamp, P. (1996). Towards a Science of Complexity in Spatial-Economic Systems. In: van den Bergh, J.C.J.M., Nijkamp, P., Rietveld, P. (eds) Recent Advances in Spatial Equilibrium Modelling. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80080-1_18

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  • DOI: https://doi.org/10.1007/978-3-642-80080-1_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-80082-5

  • Online ISBN: 978-3-642-80080-1

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