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More memory under evolutionary learning may lead to chaos

Author

Listed:
  • Cees Diks

    (CeNDEF - Center for Nonlinear Dynamics in Economics and Finance - UvA - University of Amsterdam [Amsterdam] = Universiteit van Amsterdam)

  • Cars Hommes

    (CeNDEF - Center for Nonlinear Dynamics in Economics and Finance - UvA - University of Amsterdam [Amsterdam] = Universiteit van Amsterdam)

  • Paolo Zeppini

    (CeNDEF - Center for Nonlinear Dynamics in Economics and Finance - UvA - University of Amsterdam [Amsterdam] = Universiteit van Amsterdam, TU/e - Eindhoven University of Technology [Eindhoven])

Abstract

We show that an increase of memory of past strategy performance in a simple agent-based innovation model, with agents switching between costly innovation and cheap imitation, can be quantitatively stabilising while at the same time qualitatively destabilising. As memory in the fitness measure increases, the amplitude of price fluctuations decreases, but at the same time a bifurcation route to chaos may arise. The core mechanism leading to the chaotic behaviour in this model with strategy switching is that the map obtained for the system with memory is a convex combination of an increasing linear function and a decreasing non-linear function.

Suggested Citation

  • Cees Diks & Cars Hommes & Paolo Zeppini, 2013. "More memory under evolutionary learning may lead to chaos," Post-Print hal-04575563, HAL.
    • Handle: RePEc:hal:journl:hal-04575563
    DOI: 10.1016/j.physa.2012.10.045
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    References listed on IDEAS

    as
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    Cited by:

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    9. Cavalli, Fausto & Naimzada, Ahmad, 2015. "A tâtonnement process with fading memory, stabilization and optimal speed of convergence," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 116-129.
    10. Lamantia, F. & Negriu, A. & Tuinstra, J., 2016. "Evolutionary Cournot competition with endogenous technology choice: (in)stability and optimal policy," CeNDEF Working Papers 16-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.

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