Skip to main content

Nonlinear Evolution of Socioeconomic and Spatial Systems

  • Chapter
Nonlinear Evolution of Spatial Economic Systems

Abstract

“Evolution, or order of process, is more than just a paradigm for the biological domain, it is a view of how a totality that hangs together in all of its interactive processes moves” (Jantsch, 1976, p. 9). The evolutionary paradigm is recently coming to the fore in modern economic and social sciences as a reaction against conventional theories aiming to reduce many complex phenomena to an equilibrium projection, system predictability and hierarchical control. In this context, the present volume aims to offer new insights into evolving complex socioeconomic modelling approaches by bringing together various advances and recent methodologies — emerging from different disciplines but applicable to dynamical spatial economics — which seem capable of improving our understanding and our design of structural (e.g. ‘nested’) principles of socioeconomic life such as (non)-equilibrium, (non)-predictability, (un)certainty, adaptiveness and complexity.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Allen, R.G.D., 1959, Mathematical Economics, MacMillan, London (2nd edition).

    Google Scholar 

  • Allen, P. and M. Sanglier, 1981, Urban Evolution, Self-Organization, and Decision-Making, Environment and Planning A, vol. 13, pp. 167–183.

    Article  Google Scholar 

  • Andersson, A.E. and D.F. Batten, 1988, Creative Nodes, Logistical Networks and the Future of the Metropolis, Transportation, vol. 14, pp. 281–293.

    Google Scholar 

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

    Google Scholar 

  • Batty, M. and P.A. Longley, 1986, The Fractal Simulation of Urban Structure, Environment and Planning A, vol. 18, pp. 1143–1179.

    Article  Google Scholar 

  • Boulding, K.E., 1978, Ecodynamics: A New Theory of Social Evolution, Sage, Beverly Hills.

    Google Scholar 

  • Brock, W.A., 1986, Distinguishing Random and Deterministic Systems: Abridged Version, Journal of Economic Theory, vol. 40, pp. 168–195.

    Article  Google Scholar 

  • Camagni, R., L. Diappi and G. Leonardi, 1986, Urban Growth and Decline in a Hierarchical System, Regional Science and Urban Economics, vol. 15, pp. 145–160.

    Article  Google Scholar 

  • Casti, J., 1979, Connectivity, Complexity, and Catastrophe in Large-Scale Systems, J. Wiley, New York.

    Google Scholar 

  • Crilly, T., 1991, The Roots of Chaos. A Brief Guide. In Crilly, A.J., R.A. Earnshaw and H. Jones (eds.), Fractals and Chaos, Springer-Verlag, Berlin.

    Chapter  Google Scholar 

  • Darwin, C., 1859, The Origin of Species, Penguin, Harmondsworth.

    Google Scholar 

  • Davies, P.C.W., 1992, The Physics of Complex Organization, Theoretical Biology. Epigenetic and Evolutionary Order from Complex Systems (Goodwin B. and P. Saunders, eds.), John Hopkins Press Ltd., London, pp. 101–111.

    Google Scholar 

  • Day, R.H., 1985, Dynamical Systems Theory and Complicated Economic Behaviour, Environment and Planning B, vol. 2, pp. 55–64.

    Google Scholar 

  • Day, R.H. and J.-L. Walter, 1990, Economic Growth in the Very Long Run, in: Barnett, W.A., J. Geveke and K. Shell (eds.), Economic Complexity; Chaos, Sunspots, Bubbles and Nonlinearity, Cambridge University Press, Cambridge, pp. 253–289.

    Google Scholar 

  • Degn, H., A.V. Holden and L.F. Olsen (eds.), 1987, Chaos in Biological Systems, Plenum Press, New York.

    Google Scholar 

  • Dendrinos, D.S. and H. Mullally, 1985, Urban Evolution. Studies in the Mathematical Ecology of Cities, Oxford University Press, Oxford.

    Google Scholar 

  • Dendrinos, D.S. and J.B. Rosser, 1992, Fundamental Issues in Non Linear Urban Population Dynamic Models, The Annals of Regional Science, vol. 26, no. 2, pp. 111–134.

    Article  Google Scholar 

  • De Palma, A. and C. Lefèvre, 1987, The Theory of Deterministic and Stochastic Compartmental Models and its Applications, in C.S. Bertuglia, G. Leonardi, S. Occelli, G.A. Rabino, R. Tadei and A.G. Wilson (eds.), Urban Systems: Contemporary Approaches to Modeling, Croom Helm, London, pp. 490–540.

    Google Scholar 

  • Eckmann, J.P. and D. Ruelle, 1985, Ergodic Theory of Chaos and Strange Attractors, Review of Modern Physics, vol. 57, no. 3, pp. 617–656.

    Article  Google Scholar 

  • Feigenbaum, H.J., 1978, Quantitative Universitality for a Class of Non-Linear Transformations, Journal of Statistical Planning, vol. 19, pp. 25–52.

    Article  Google Scholar 

  • Fischer, E.O. and W. Jammernegg, 1986, Empirical Investigation of a Catastrophe Exclusion of the Phillips Curve, Review of Economics and Statistics, vol. 68, no. 1, pp. 9–17.

    Article  Google Scholar 

  • Fischer, M.M., P. Nijkamp and Y.Y. Papegeorgiou, 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. and T. Stengos, 1988, Chaotic Dynamics in Economic Time-Series, Journal of Economic Surveys, vol. 2, no. 2, pp. 103–133.

    Article  Google Scholar 

  • Frankhauser, P., 1991, Aspects Fractals des Structures Urbaines, L’Espace Géographique, no. 1, pp. 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 

  • Glass, L., M.R. Guevera, M.R. Shrier and R. Perez, 1983, Bifurcation and Chaos in a Periodically Stimulated Cardiac Oscillator, Physica D, vol. 7, pp. 89–101.

    Article  Google Scholar 

  • Goodwin, B.C., 1992, Evolution and the Generative Order, Theoretical Biology. Epigenetic and Evolutionary Order from Complex Systems (Goodwin B. and P. Saunders, eds.), John Hopkins Press Ltd., London, pp. 89–100.

    Google Scholar 

  • Grassberger, P. and I. Procaccia, 1983a, Measuring the Strangeness of Strange Attractors, Physica D, vol. 9, pp. 189–208.

    Article  Google Scholar 

  • Grassberger, P. and I. Procaccia, 1983b, Estimation of the Kolmogorov Entropy from a Chaotic Signal, Physical Review A, vol. 28, pp. 2591–2593.

    Article  Google Scholar 

  • Grübler, A. and Nakicenovic, 1991, Evolution of Transport Systems: Past and Future, RR-91–8, International Institute For Applied Systems Analysis, Laxenburg.

    Google Scholar 

  • Guckenheimer, J., 1979, Sensitive Dependence to Initial Conditions for One-Dimensional Maps, Communications in Mathematical Physics, vol. 70, 1979, pp. 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, Scientific Publication. Co., Singapore.

    Google Scholar 

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

    Google Scholar 

  • Holden, A.V. and M.A. Muhamad, 1986, A Graphical Zoo of Strange and Peculiar Attractors, in: A.V. Holden (ed.), Chaos, Manchester University Press, Manchester, pp. 15–35.

    Google Scholar 

  • Jantsch, E., 1976, Self-Transcendence: New Light on the Evolution Paradigm, Evolution and Consciousness. Human Systems in Transition (Jantsch E. and C.H. Waddington, eds.), Addison Wesley, Reading, Massachussetts, pp. 9–10.

    Google Scholar 

  • Jantsch, E., 1980, The Self-Organizing Universe, Pergamon Press, Oxford.

    Google Scholar 

  • Johansson, B. and P. Nijkamp, 1987, Analysis of Episodes in Urban Event Histories, Spatial Cycles (Van den Berg, L., L.S. Burns and W. H. Klaassen, eds.), Gower, Aldershot, pp. 43–66.

    Google Scholar 

  • Kelsey, D., 1988, The Economics of Chaos or the Chaos of the Economics, Oxford University Papers, vol. 40, pp. 1–3.

    Google Scholar 

  • Kurths, J. and H. Herzel, 1987, An Attractor in a Solar Time Series, Physica D, vol. 25, pp. 165–172.

    Article  Google Scholar 

  • Li, T.Y. and J.A. Yorke, 1975, Period Three Implies Chaos, American Mathematical Monthly, vol. 82, no. 10, pp. 985–992.

    Article  Google Scholar 

  • Lichtenberg, A.J. and M.A. Lieberman, 1983, Regular and Stochastic Motion, Springer-Verlag, Berlin.

    Google Scholar 

  • Lombardo, S.T. and G.A. Rabino, 1983, Some Simulations of a Central Place Theory Model, Sistemi Urbani, vol. 5, pp. 315–332.

    Google Scholar 

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

    Google Scholar 

  • Lotka, A., 1920, Analytical Notes on Certain Rhythmic Relation in Organic Systems, Proceedings of the National Academy of Sciences, United States, vol. 6, pp. 410–415.

    Google Scholar 

  • Mandelbrot, B., 1977, The Fractal Geometry of Nature, V. H. Dreeman and Company, New York.

    Google Scholar 

  • Manneville, P. and Y. Pomeau, 1979, Intermittency and the Lorenz Model, Physics Letters A, vol. 75, no. 1/2, pp. 1–2.

    Article  Google Scholar 

  • Marsden, J.E. and M. McCracken, 1976, The Hopf Bifurcation and its Applications, Springer-Verlag, Berlin.

    Book  Google Scholar 

  • Marshall, A., 1920, Principles of Economics, Macmillan, London.

    Google Scholar 

  • May, R.M., 1973, Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton.

    Google Scholar 

  • May, R., 1976, Simple Mathematical Models with Very Complicated Dynamics, Nature, vol. 261, pp. 459–467.

    Article  Google Scholar 

  • Meadows, D.L. and D.H. Meadows (eds.), 1973, Toward Global Equilibrium: Collected Papers, Wright-Allen Press, Cambridge, Mass.

    Google Scholar 

  • Medio, A., 1979, Teoria Non Lineare del Ciclo Economico, Il Mulino, Bologna.

    Google Scholar 

  • Mees, A., 1975, The Revival of Cities in Medieval Europe: An Application of Catastrophe Theory, Regional Science and Urban Economics, vol. 5, pp. 403–425.

    Article  Google Scholar 

  • Newhouse, S., D. Ruelle and F. Takens, 1978, Occurrence of Strange Axiom-A Attractors near Quasiperiodic Flow or T’ m 3, Communications in Mathematics Physics, vol. 64, pp. 35–40.

    Article  Google Scholar 

  • Nicolis, G., 1986, Dissipative Systems, Reports on Progress in Physics, vol. 49, pp. 873–949.

    Article  Google Scholar 

  • Nicolis, G., and I. Prigogine, 1977, Self-Organization in Nonequilibrium Systems, Wiley, New York.

    Google Scholar 

  • Nijkamp, P., 1987, Long Term Economic Fluctuations: A Spatial View, Socio-Economic Planning Sciences, vol. 21, no. 3, 189–197.

    Article  Google Scholar 

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

    Google Scholar 

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

    Book  Google Scholar 

  • Nijkamp, P. and A. Reggiani, 1992b, Spatial Competition and Ecologically Based Socio-Economic Models, Socio Spatial Dynamics, vol. 3, No. 2, pp. 89–109.

    Google Scholar 

  • Nijkamp. P. and A. Reggiani, 1992c, Impacts of Changing Environmental Conditions on Transport Systems, Research Memorandum 1992–51, Dept. of Economics, Free University, Amsterdam.

    Google Scholar 

  • Nusse, H.E., 1987, Asymptotically Periodic Behaviour in the Dynamics of Chaotic Mapping, SIAM Journal of Applied Mathematics, vol. 47, pp. 498–515.

    Article  Google Scholar 

  • Peitgen, H.O. and P.H. Richter, 1986, The Beauty of Fractals, Springer-Verlag, Berlin.

    Book  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Power and Air, Biological Bulletin, vol. 25, pp. 79–120.

    Google Scholar 

  • Prigogine, I. and I. Stengers, 1984, Order out of Chaos, Fontana, London.

    Google Scholar 

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

    Google Scholar 

  • Rosser, J.B., 1991, From Catastrophe to Chaos: A General Theory of Economic Discontinuities, Kluwer Academic Publishers, Dordrecht.

    Book  Google Scholar 

  • Ruelle, D. and F. Takens, 1971, On the Nature of Turbulence, Communications in Mathematical Physics, vol. 20, pp. 167–192.

    Article  Google Scholar 

  • Russel, E.S., 1915, Form and Function, Murray, London.

    Google Scholar 

  • Samuelson, P.A., 1947, Foundations of Economic Analysis, Harvard University Press, Cambridge, Mass.

    Google Scholar 

  • Schaffer, W.M. and M. Kot, 1985, Nearly One-Dimensional Dynamics in an Epidemic, Journal of Theoretical Biology, vol. 112, pp. 403–427.

    Article  Google Scholar 

  • Schumpeter, J.A., 1934, The Theory of Economic Development, Harvard University Press, Cambridge, Mass.

    Google Scholar 

  • Schuster, H.G., 1988, Deterministic Chaos, VCH, Veinheim.

    Google Scholar 

  • Swinney, H., 1983, Observations of Order and Chaos in Non-Linear Systems, Physica D, vol. 7, pp. 3–15.

    Article  Google Scholar 

  • Thom, R., 1972, Structural Stability and Morphogenesis, Addison-Wesley, Reading.

    Google Scholar 

  • Varian, H., 1978, Catastrophe Theory and the Business Cycle, Economic Inquiry, vol. 17, pp. 14–28.

    Article  Google Scholar 

  • Vendrik, M.C.M., 1990, Habits, Histeresis and Catastrophes in Labor Supply, Research Memorandum 90–031, Department of Economics, University of Limburg, Maastricht.

    Google Scholar 

  • Volterra, V., 1931, Lecons sur la theorie mathematique de la lutte pour la vie, Gauthier-Villars, Paris.

    Google Scholar 

  • Waddington, C.H., 1957, The Strategy of the Genes, Allen and Unwin.

    Google Scholar 

  • Walras, L., 1874, Eléments D’Economies Pure, L. Corbaz, Lausanne (English Translation: W. Jaffe, Elements of Pure Economics, Allen and Unwin, London, 1954 ).

    Google Scholar 

  • Wilson, A.G., 1981, Catastrophe Theory and Bifurcation, Croom Helm, London.

    Google Scholar 

  • Wright, S., 1931, Evolution in Mendelian Population, Genetics, vol. 16, pp. 97–189.

    Google Scholar 

  • Zeeman, F.C., 1977, Catastrophe Theory: Selected Papers 1972–1977, Addison-Wesley, Reading.

    Google Scholar 

  • Zhang, W.B., 1990, Economic Dynamics, Springer-Verlag, Berlin.

    Google Scholar 

  • Zhang, W.B., 1991, Synergetic Economics, Springer-Verlag, Berlin.

    Book  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin · Heidelberg

About this chapter

Cite this chapter

Nijkamp, P., Reggiani, A. (1993). Nonlinear Evolution of Socioeconomic and Spatial Systems. In: Nijkamp, P., Reggiani, A. (eds) Nonlinear Evolution of Spatial Economic Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78463-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-78463-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-78465-1

  • Online ISBN: 978-3-642-78463-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics