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

By Tomoyuki Miyaji, Isamu Ohnishi, Atsushi Tero, and Toshiyuki Nakagaki

Int. J. Dynamical Systems and Differential Equations, Vol. 1, No. 3, 2008

The abstract is the following: 

In this paper we study a mathematical model describing behavior 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.

Article: Failure to the shortest path decision of an adaptive transport network with double edges in Plasmodium system Journal: International Journal of Dynamical Systems and Differential Equations (IJDSDE) 2008 Vol.1 No.3 pp.210 - 219 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. Inderscience Publishers - linking academia, business and industry through research

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