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Plasmodium of true slime mold, Physarum polycephalum, is an amoeboidorganism, which spreads with developing tubular network structure and crawls ontwo-dimensional plane with oscillating the cell thickness. The plasmodiumtransforms its tubular network structure to adapt to the environment. To revealthe effect of the network structure on the oscillating behavior of theplasmodium, we constructed coupled map systems on two-dimensional weightednetworks as models of the plasmodium, and investigated the relation between thedistribution of weights on the network edges and the synchronization in thesystem. We found the probability that the system shows phase synchronizationchanges drastically with the weight distribution even if the total weight isconstant. This implies the oscillating patterns observed in the plasmodium arecontrolled by the tube widths or cross-sections in the tubular networks.

Collective behavior in coupled dynamical systems on two-dimensional  weighted networks: A step toward understanding adaptive behavior of true  slime mold