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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.

Suggested Citation

  • 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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    File URL: https://doi.org/10.1111/j.1468-5876.2007.00382.x
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    Cited by:

    1. Alain Raybaut, 2019. "A first French episode in the renewal of nonlinear theory of economic cycles (1978-1985)," Working Papers halshs-02377359, HAL.
    2. Hiroki Murakami, 2019. "A note on the “unique” business cycle in the Keynesian theory," Metroeconomica, Wiley Blackwell, vol. 70(3), pages 384-404, July.
    3. 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.
    4. Murakami, Hiroki & Zimka, Rudolf, 2020. "On dynamics in a two-sector Keynesian model of business cycles," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    5. 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.
    6. K. Vela Velupillai, 2012. "Ferdinando Targetti - In Memorium Scholar, Friend, Colleague- and a Gentleman," ASSRU Discussion Papers 1208, ASSRU - Algorithmic Social Science Research Unit.
    7. 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.
    8. K.Vela Velupillai, 2012. "The Geometrist of Economic Dynamics: Richard Goodwin's Birth Centennial," ASSRU Discussion Papers 1216, ASSRU - Algorithmic Social Science Research Unit.
    9. 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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