Cuspoidal Nets

  • Ralph Abraham
Part of the International Economic Association book series (IEA)

Abstract

The ubiquitous cusp catastrophe has been pressed into service by Zeeman as a rough qualitative model for many dynamical systems in the sciences, including a democratic nation. The extension to two nations has been made by Kadyrov, who discovered an interesting oscillation in this context. Here we speculate on the properties of connectionist networks of cusps, which might be used to model social and economic systems.

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Notes

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    3. Ralph H. Abraham, ‘Cellular Dynamical Systems’, pp. 7–8 in Mathematics and Computers in Biomedical Applications, Proc. IMACS World Congress, Olso, 1985, ed. J. Eisenfeld and C. DeLisi, North-Holland, Amsterdam (1986).Google Scholar
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    6. Ralph H. Abraham and Christopher D. Shaw, Dynamics, the Geometry of Behavior, Four vols., Santa Cruz, CA: Aerial Press, 1982–8).Google Scholar
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    8.M. N. Kadyrov, ‘A Mathematical Model of the Relations between Two States’, Global Development Processes 3 Institute for Systems Studies, (1984).Google Scholar
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    9.Tim Poston and Ian Stewart, Catastrophe Theory and its Applications (London: Pitman, 1978).Google Scholar
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    10. Steve Smale, ‘A Mathematical Model of Two Cells via Turing’s Equation’, in M. MacCracken (ed.) The Hopf Bifurcation and its Applications (New York: Springer, 1976).Google Scholar
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Copyright information

© International Economic Association 1991

Authors and Affiliations

  • Ralph Abraham
    • 1
  1. 1.UNIVERSITY OF CALIFORNIACALIFORNIAUSA

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