Regular Article

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

Aix Marseille Univ., Université de Toulon, CNRS, CPT, Marseille, France

^a e-mail: olivi.bui@gmail.com

Received: 26 February 2019
Received in final form: 2 May 2019
Published online: 8 July 2019

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.