TY - JOUR
T1 - Failure to the shortest path decision of an adaptive transport network with double edges in Plasmodium system
AU - Miyaji, Tomoyuki
AU - Ohnishi, Isamu
AU - Tero, Atsushi
AU - Nakagaki, Toshiyuki
PY - 2008/7
Y1 - 2008/7
N2 - 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.
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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U2 - 10.1504/IJDSDE.2008.019683
DO - 10.1504/IJDSDE.2008.019683
M3 - Article
AN - SCOPUS:48849090162
SN - 1752-3583
VL - 1
SP - 210
EP - 219
JO - International Journal of Dynamical Systems and Differential Equations
JF - International Journal of Dynamical Systems and Differential Equations
IS - 3
ER -