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.
1. Dedicated to Christopher Zeeman on his sixtieth birthday.
2. It is a pleasure to acknowledge the generosity of Chris Zeeman, Tim Poston, and Gottfried Mayer-Kress in sharing their ideas; Peter Brecke for a translation of Kadyrov’s paper; and the University of California’s INCOR program for financial support of this work, in connection with a modelling project on international stability, jointly with Gottfried Mayer-Kress. Thanks also to John Corliss and John Dorband at the NASA Goddard Space Flight Center for introducing me to the Massively Parallel Processor.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes
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).
5. E. Christopher Zeeman, ‘Duffing’s Equation in Brain Modelling’, pp. 293-3Q0 in E. Christopher Zeeman (ed.) Catastrophe Theory (Reading, MA: Addison-Wesley, 1977).
6. Ralph H. Abraham and Christopher D. Shaw, Dynamics, the Geometry of Behavior, Four vols., Santa Cruz, CA: Aerial Press, 1982–8).
7. C. A. Isnard and E. C. Zeeman, ‘Some Models from Catastrophe Theory in the Social Sciences’, (E. C. Zeeman, Catastrophe Theory, New York: Addison-Wesley, 1977) pp. 303–59.
8.M. N. Kadyrov, ‘A Mathematical Model of the Relations between Two States’, Global Development Processes 3 Institute for Systems Studies, (1984).
9.Tim Poston and Ian Stewart, Catastrophe Theory and its Applications (London: Pitman, 1978).
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).
J. J. Hopfield, ‘Neural Networks and Physical Systems with Emergent Collective Computational Abilities’, Proceedings of the National Academy of Science, USA (1982) 79, pp. 2554–8.
Author information
Authors and Affiliations
Editor information
Copyright information
© 1991 International Economic Association
About this chapter
Cite this chapter
Abraham, R. (1991). Cuspoidal Nets. In: Thygesen, N., Velupillai, K., Zambelli, S. (eds) Business Cycles. International Economic Association. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-11570-9_3
Download citation
DOI: https://doi.org/10.1007/978-1-349-11570-9_3
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-11572-3
Online ISBN: 978-1-349-11570-9
eBook Packages: Palgrave Economics & Finance CollectionEconomics and Finance (R0)