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Pattern Formation and Functionality in Swarm Models

Author

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  • Erik M. Rauch
  • Mark M. Millonas
  • Dante R. Chialvo

Abstract

We explore a simplified class of models we call swarms, which are inspired by the collective behavior of social insects. We perform a mean-field stability analysis and numerical simulations of the model. Several interesting types of behavior emerge in the vicinity of a second-order phase transition in the model, including the formation of stable lines of traffic flow, and memory reconstruction and bootstrapping. In addition to providing an understanding of certain classes of biological behavior, these models bear a generic resemblance to a number of pattern formation processes in the physical sciences.

Suggested Citation

  • Erik M. Rauch & Mark M. Millonas & Dante R. Chialvo, 1995. "Pattern Formation and Functionality in Swarm Models," Working Papers 95-08-073, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:95-08-073
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    Cited by:

    1. Czirók, András & Vicsek, Tamás, 2000. "Collective behavior of interacting self-propelled particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 17-29.
    2. Choi, So Eun & Jang, Hyun Jin & Lee, Kyungsub & Zheng, Harry, 2021. "Optimal market-Making strategies under synchronised order arrivals with deep neural networks," Journal of Economic Dynamics and Control, Elsevier, vol. 125(C).
    3. García Cantú Ros, A. & Antonopoulos, Ch.G. & Basios, V., 2011. "Emergence of coherent motion in aggregates of motile coupled maps," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 574-586.
    4. Hyun Jin Jang & Kiseop Lee & Kyungsub Lee, 2020. "Systemic risk in market microstructure of crude oil and gasoline futures prices: A Hawkes flocking model approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(2), pages 247-275, February.

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