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More memory under evolutionary learning may lead to chaos

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  • Diks, Cees
  • Hommes, Cars
  • Zeppini, Paolo

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

  • Diks, Cees & Hommes, Cars & Zeppini, Paolo, 2013. "More memory under evolutionary learning may lead to chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 808-812.
  • Handle: RePEc:eee:phsmap:v:392:y:2013:i:4:p:808-812 DOI: 10.1016/j.physa.2012.10.045
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. He, Kaijian & Xu, Yang & Zou, Yingchao & Tang, Ling, 2015. "Electricity price forecasts using a Curvelet denoising based approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 425(C), pages 1-9.
    2. Agliari, Anna & Naimzada, Ahmad & Pecora, Nicolò, 2017. "Dynamic effects of memory in a cobweb model with competing technologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 340-350.
    3. Kukacka, Jiri & Barunik, Jozef, 2013. "Behavioural breaks in the heterogeneous agent model: The impact of herding, overconfidence, and market sentiment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5920-5938.
    4. He, Kaijian & Lu, Xingjing & Zou, Yingchao & Keung Lai, Kin, 2015. "Forecasting metal prices with a curvelet based multiscale methodology," Resources Policy, Elsevier, vol. 45(C), pages 144-150.

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