Failure to the shortest path decision of an adaptive transport network with double edges in Plasmodium system

Tomoyuki Miyaji; Isamu Ohnishi; Atsushi Tero; Toshiyuki Nakagaki

doi:10.1504/IJDSDE.2008.019683

Failure to the shortest path decision of an adaptive transport network with double edges in Plasmodium system

Tomoyuki Miyaji, Isamu Ohnishi, Atsushi Tero, Toshiyuki Nakagaki

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper we study a mathematical model describing behaviour of Physarum polycephalum proposed by Tero et al. (2007). In the case of linear adaptive term, it has been proved that the model must solve the shortest path problem mathematically rigorously on a general planar graph in Miyaji and Ohnishi (2007, 2008). However, in a laboratory, P. polycephalum sometimes makes a mistake, for example, when there is a 'double-edge' in a graph. We study the case mathematically to show both why and how P. polycephalum makes a mistake.

Original language	English
Pages (from-to)	210-219
Number of pages	10
Journal	International Journal of Dynamical Systems and Differential Equations
Volume	1
Issue number	3
DOIs	https://doi.org/10.1504/IJDSDE.2008.019683
Publication status	Published - Jul 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Engineering(all)
Discrete Mathematics and Combinatorics
Control and Optimization

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10.1504/IJDSDE.2008.019683

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abstract = "In this paper we study a mathematical model describing behaviour of Physarum polycephalum proposed by Tero et al. (2007). In the case of linear adaptive term, it has been proved that the model must solve the shortest path problem mathematically rigorously on a general planar graph in Miyaji and Ohnishi (2007, 2008). However, in a laboratory, P. polycephalum sometimes makes a mistake, for example, when there is a 'double-edge' in a graph. We study the case mathematically to show both why and how P. polycephalum makes a mistake.",

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AB - In this paper we study a mathematical model describing behaviour of Physarum polycephalum proposed by Tero et al. (2007). In the case of linear adaptive term, it has been proved that the model must solve the shortest path problem mathematically rigorously on a general planar graph in Miyaji and Ohnishi (2007, 2008). However, in a laboratory, P. polycephalum sometimes makes a mistake, for example, when there is a 'double-edge' in a graph. We study the case mathematically to show both why and how P. polycephalum makes a mistake.

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Failure to the shortest path decision of an adaptive transport network with double edges in Plasmodium system

Abstract

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