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Growth of a tree with allocation rules. Part 1: kinematics

Author

Listed:
  • Olivier Bui

    (Aix Marseille Univ., Université de Toulon, CNRS, CPT)

  • Xavier Leoncini

    (Aix Marseille Univ., Université de Toulon, CNRS, CPT)

Abstract

A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on a tree-like network, and the network transports the resource it needs to build itself. Some general results are given on the viability tree-like networks which ressources are produced at the leaves while having maintenance and growing costs at each node. Some analytical studies and numerical surveys of the model in “simple” situations are made. The different outcomes are discussed and possible extensions of the model are then discussed. Graphical abstract

Suggested Citation

  • Olivier Bui & Xavier Leoncini, 2019. "Growth of a tree with allocation rules. Part 1: kinematics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(7), pages 1-12, July.
    • Handle: RePEc:spr:eurphb:v:92:y:2019:i:7:d:10.1140_epjb_e2019-100111-5
    DOI: 10.1140/epjb/e2019-100111-5
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    References listed on IDEAS

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    1. Jens Leth Hougaard, 2009. "Sharing in Networks," Springer Books, in: An Introduction to Allocation Rules, chapter 5, pages 125-152, Springer.
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    1. Olivier Bui & Xavier Leoncini, 2021. "Growth of a tree with allocations rules: part 2 dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-13, January.

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    Statistical and Nonlinear Physics;

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