A simplistic dynamic circuit analogue of adaptive transport networks in true slime mold

Abstract

This paper presents a simplistic dynamic circuit analogue for an adaptive transport network model in true slime mold by Tero et al. This circuit analogue model is derived from Tero's model through nontrivial simplification under certain assumptions, and it realizes less computational complexity through a reduction of the number of variables. Despite of its simplicity, systematic simulations confirm that the shortest path search task is efficiently accomplished with this model; (i) the shortest path is always identified, for various random networks; (ii) if there are multiple, competing shortest paths in the network, they are simultaneously identified; and (iii) for random deletions of a link in the shortest path, a new shortest path is quickly identified accordingly. The model proposed here is easily implemented on the circuit simulator SPICE for instance, and hence the path search time will be further reduced with certain numerical devices including automatic adaptive numerical integration schemes as well as an acceleration method proposed in the end of the paper.