Current-reinforced random walks for constructing transport networks

Qi Ma, Anders Johansson, Atsushi Tero, Toshiyuki Nakagaki, David J.T. Sumpter

研究成果: Contribution to journalArticle査読

24 被引用数 (Scopus)


Biological systems that build transport networks, such as trail-laying ants and the slime mould Physarum, can be described in terms of reinforced random walks. In a reinforced random walk, the route taken by 'walking' particles depends on the previous routes of other particles. Here, we present a novel form of random walk in which the flow of particles provides this reinforcement. Starting from an analogy between electrical networks and random walks, we show how to include current reinforcement. We demonstrate that current-reinforcement results in particles converging on the optimal solution of shortest path transport problems, and avoids the selfreinforcing loops seen in standard density-based reinforcement models. We further develop a variant of the model that is biologically realistic, in the sense that the particles can be identified as ants and their measured density corresponds to those observed in maze-solving experiments on Argentine ants. For network formation, we identify the importance of nonlinear current reinforcement in producing networks that optimize both network maintenance and travel times. Other than ant trail formation, these random walks are also closely related to other biological systems, such as blood vessels and neuronal networks, which involve the transport of materials or information. We argue that current reinforcement is likely to be a common mechanism in a range of systems where network construction is observed.

ジャーナルJournal of the Royal Society Interface
出版ステータス出版済み - 3 6 2013

All Science Journal Classification (ASJC) codes

  • バイオテクノロジー
  • 生物理学
  • バイオエンジニアリング
  • 生体材料
  • 生化学
  • 生体医工学


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