IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

Dynamical Coupling, Nonlinear Accelerator and the Persistence of Business Cycles

  • Stefano Zambelli

Many of the research questions and research programs that were posed and suggested by Richard Goodwin are still highly relevant for various methodological, empirical and theoretical reasons. In this paper, we address the issue of whether highly articulated and complex economic interactions can be represented by a simplified low dimensional model. We follow the valuable insight offered by Goodwin (1947) concerning the importance of dynamical coupling and the potential role of analog and/or digital computers in studying them fruitfully. Here, we extend the nonlinear, flexible accelerator - dynamic multiplier model of business cycle by Goodwin (1951), to the case in which these economies are coupled through trade. The dynamics implied by the coupling are studied in analogy with the well known Fermi-Pasta-Ulam problem (Fermi et al., 1955). We show that for nonlinear economies, even when they are exactly the same, i.e. having the same structural behavioral equations, the very rich dynamics depend crucially on the initial conditions. This result is somewhat unexpected.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by ASSRU - Algorithmic Social Science Research Unit in its series ASSRU Discussion Papers with number 1214.

in new window

Date of creation: 2012
Date of revision:
Handle: RePEc:trn:utwpas:1214
Contact details of provider: Postal:
Via Inama 5, 38100 Trento

Phone: +39-461-882201
Fax: +39-461-882222
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. K. Vela Velupillai, 2008. "The Mathematization of Macroeconomics: A Recursive Revolution," Department of Economics Working Papers 0807, Department of Economics, University of Trento, Italia.
  2. V. Ragupathy & K. Vela Velupillai, 2012. "Existence Proofs in Nonlinear Endogenous Theories of the Business Cycle on the Plane -- The Origins," ASSRU Discussion Papers 1210, ASSRU - Algorithmic Social Science Research Unit.
  3. Kumaraswamy Velupillai, . "The Computable Approach to Economics," Working Papers _005, University of California at Los Angeles, Center for Computable Economics.
  4. Stefano Zambelli, 2011. "Flexible Accelerator Economic Systems As Coupled Oscillators," Journal of Economic Surveys, Wiley Blackwell, vol. 25(3), pages 608-633, 07.
  5. Ragnar Frisch, 1932. "Capital Production and Consumer-Taking: A Rejoinder," Journal of Political Economy, University of Chicago Press, vol. 40, pages 253.
  6. K. Vela Velupillai, 2005. "The impossibility of an Effective Theory of Policy in a Complex Economy," Working Papers 0094, National University of Ireland Galway, Department of Economics, revised 2005.
  7. Kumaraswamy Velupillai, 2003. "Economics and the complexity vision: chimerical partners or elysian adventurers," Department of Economics Working Papers 0307, Department of Economics, University of Trento, Italia.
  8. K. Vela Velupillai & Stefano Zambelli, 2011. "Computing in Economics," Chapters, in: The Elgar Companion to Recent Economic Methodology, chapter 12 Edward Elgar Publishing.
  9. Stefano Zambelli, 2007. "A Rocking Horse That Never Rocked: Frisch's “Propagation Problems and Impulse Problems”," History of Political Economy, Duke University Press, vol. 39(1), pages 145-166, Spring.
  10. Stefano Zambelli, 2010. "Coupled Dynamics in the Phillips Machine Model of the Macroeconomy," ASSRU Discussion Papers 1011, ASSRU - Algorithmic Social Science Research Unit.
  11. Ragnar Frisch, 1932. "Capital Production and Consumer-Taking: A Final Word," Journal of Political Economy, University of Chicago Press, vol. 40, pages 694.
  12. Velupillai, K. Vela, 1998. "The vintage economist," Journal of Economic Behavior & Organization, Elsevier, vol. 37(1), pages 1-31, September.
  13. Ragnar Frisch, 1931. "The Interrelation Between Capital Production and Consumer-Taking," Journal of Political Economy, University of Chicago Press, vol. 39, pages 646.
  14. Velupillai K. Vela, 2011. "The Phillips Machine, the Analogue Computing Tradition in Economics and Computability," Economia politica, Società editrice il Mulino, issue 1, pages 39-62.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:trn:utwpas:1214. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.