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By stochastic simulation, we investigate the spatial pattern in the biological system composed of three competing species. Topological defects are introduced to explain the pattern formation in this system. The spatial dimension d determines the nature of defects such as kinks, vortices, and strings. When J =2,3, the system approaches the stationary state, where the peculiar defect configuration is found.

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SynopsisIn a recent paper, we developed a thermodynamic theory on the complex coacervation in the absence of low molecular ions, under the assumption that the coacervation is a condensation phenomenon of aggregates of polyanion and polycation in the aqueous solution, by obtaining the interaction potential Us between these aggregates on the basis of Flory's method.In this paper, we have extended the theory to a more complicated phenomenon of the counterion-containing solutions. This treatment has led the interaction potential having an additional contribution to Us resulting from an entropy increase by the counterion distribution.The phase diagram between solution (sol) and separated phase has been obtained as a function of the difference of charges between polyanion and polycation. It has been found that the presence of counterions sensitively suppresses the coacervation.