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JAPANESE CONTRIBUTIONS TO NONLINEAR CYCLE THEORY IN THE 1950s

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  • K. VELA VELUPILLAI

Abstract

In the early 1950s pioneering contributions were made to the nonlinear theory of Keynesian macrodynamics by Shinichi Ichimura, Michio Morishima and Takuma Yasui. They were the first to formally investigate the existence, stability and uniqueness of limit cycles in macrodynamics. An attempt is made to place the contributions of this Japanese school of nonlinear trade cycle theorists within the context and development of math‐ematical economics in early post‐war Japan. As an additional, although minor, exercise, Morishima's model of the cycle is simplified and generalized to show, using the Andronov‐Hopf bifurcation theorem, the existence of a periodic orbit.

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  • K. Vela Velupillai, 2008. "JAPANESE CONTRIBUTIONS TO NONLINEAR CYCLE THEORY IN THE 1950s," The Japanese Economic Review, Japanese Economic Association, vol. 59(1), pages 54-74, March.
    • Handle: RePEc:bla:jecrev:v:59:y:2008:i:1:p:54-74
    DOI: 10.1111/j.1468-5876.2007.00382.x
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    1. Torre, V, 1977. "Existence of Limit Cycles and Control in Complete Keynesian System by Theory of Bifurcations," Econometrica, Econometric Society, vol. 45(6), pages 1457-1466, September.
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    5. H. Rose, 1967. "On the Non-Linear Theory of the Employment Cycle," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(2), pages 153-173.
    6. K. Vela Velupillai, 2004. "Economic Dynamics and Computation—Resurrecting the Icarus Tradition," Metroeconomica, Wiley Blackwell, vol. 55(2‐3), pages 239-264, May.
    7. Jess Benhabib & Kazuo Nishimura, 2012. "Competitive Equilibrium Cycles," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 75-96, Springer.
    8. W. W. Chang & D. J. Smyth, 1971. "The Existence and Persistence of Cycles in a Non-linear Model: Kaldor's 1940 Model Re-examined," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 37-44.
    9. Rose, Hugh, 1969. "Real and Monetary Factors in the Business Cycle," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 1(2), pages 138-152, May.
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    Cited by:

    1. Hiroki Murakami, 2019. "A note on the “unique” business cycle in the Keynesian theory," Metroeconomica, Wiley Blackwell, vol. 70(3), pages 384-404, July.
    2. V. Ragupathy & K.Vela Velupillai & Stefano Zambelli, 2012. "A Non-mathematical Non-linear Model of the Trade Cycle: Mathematical Reflections on Hugh Hudson's Classic," ASSRU Discussion Papers 1215, ASSRU - Algorithmic Social Science Research Unit.
    3. Murakami, Hiroki & Zimka, Rudolf, 2020. "On dynamics in a two-sector Keynesian model of business cycles," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. V. Ragupathy & Stefano Zambelli & K. Vela Velupillai, 2013. "A Non-linear Model of the Trade Cycle: Mathematical Reflections on Hugh Hudson's Classic," Australian Economic Papers, Wiley Blackwell, vol. 52(2), pages 115-125, June.
    5. Alain Raybaut, 2021. "A first French episode in the renewal of nonlinear theory of economic cycles," Post-Print hal-03375804, HAL.
    6. Alain Raybaut, 2019. "A First French Episode in the Renewal of Nonlinear Theory of Economic Cycles (1978-1985)," GREDEG Working Papers 2019-07, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    7. K. Vela Velupillai, 2012. "Ferdinando Targetti - In Memorium Scholar, Friend, Colleague- and a Gentleman," ASSRU Discussion Papers 1208, ASSRU - Algorithmic Social Science Research Unit.
    8. Di Matteo, Massimo, 2013. "Economic dynamics as a succession of equilibria: The path traveled by Morishima," Structural Change and Economic Dynamics, Elsevier, vol. 24(C), pages 123-129.
    9. K.Vela Velupillai, 2012. "The Geometrist of Economic Dynamics: Richard Goodwin's Birth Centennial," ASSRU Discussion Papers 1216, ASSRU - Algorithmic Social Science Research Unit.
    10. Murakami, Hiroki, 2020. "Monetary policy in the unique growth cycle of post Keynesian systems," Structural Change and Economic Dynamics, Elsevier, vol. 52(C), pages 39-49.

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