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On the existence of chaotic solutions in dynamic linear programming1This paper is a part of Keynote address entitled Nonlinear Dynamics and Economic Cycles delivered by Kazuo Nishimura at the International Congress on Modelling and Simulation held in Hobart, Australia (December 8–11, 1997) in which he gave a survey of earlier works he had done with Makoto Yano and other authors on the nonlinear dynamics in the field of optimal growth.1

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  • Nishimura, Kazuo
  • Yano, Makoto

Abstract

This paper reports our result demonstrating that chaos may emerge as a solution to a dynamic linear programming (LP) problem. At the same time, we present a parametrized dynamic nonlinear programming problem the limit of which equals that dynamic LP problem. Although it may be proved analytically that, near the limit, some solutions to the parametrized dynamic nonlinear programming problem behave chaotically, whether or not the chaotic behavior is observable is unknown in that nonlinear problem. In this study, we point it out as an open question to demonstrate the observability of chaos in the parametrized problem by simulation.

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  • Nishimura, Kazuo & Yano, Makoto, 1999. "On the existence of chaotic solutions in dynamic linear programming1This paper is a part of Keynote address entitled Nonlinear Dynamics and Economic Cycles delivered by Kazuo Nishimura at the Internat," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(4), pages 487-496.
    • Handle: RePEc:eee:matcom:v:48:y:1999:i:4:p:487-496
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    1. Kazuo Nishimura & Tadashi Shigoka & Makoto Yano, 1998. "Interior Optimal Chaos with Arbitrarily Low Discount Rates," The Japanese Economic Review, Japanese Economic Association, vol. 49(3), pages 223-233, September.
    2. Kazuo Nishimura & Makoto Yano, 2012. "Non-linear Dynamics and Chaos in Optimal Growth: An Example," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 127-150, Springer.
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    Keywords

    Dynamic LP problem; Chaos;

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