  Plasmodium of true slime mold, Physarum polycephalum, is an amoeboid
organism, which spreads with developing tubular network structure and crawls on
two-dimensional plane with oscillating the cell thickness. The plasmodium
transforms its tubular network structure to adapt to the environment. To reveal
the effect of the network structure on the oscillating behavior of the
plasmodium, we constructed coupled map systems on two-dimensional weighted
networks as models of the plasmodium, and investigated the relation between the
distribution of weights on the network edges and the synchronization in the
system. We found the probability that the system shows phase synchronization
changes drastically with the weight distribution even if the total weight is
constant. This implies the oscillating patterns observed in the plasmodium are
controlled by the tube widths or cross-sections in the tubular networks.
