Growth dynamics of domain pattern in a three-trophic population model

Pattern dynamics of a three-trophic population model was numerically investigated in a two-dimensional space. By measuring the spatial correlation function of the domain patterns, whose density was higher than 90% of the maximum density in the whole area, we found that the characteristic length scale of the ordered domain increased in time in the power law form, L(t) tφ for the super-predator and the predator, respectively. In the case of prey, there were two different growth regimes. The growth exponent changed at the crossover time t=τ. In order to investigate the geometrical features of the domain patterns, the evolution of the “fractal dimension” of the domain patterns was also studied. In the case of prey, fractal dimension decreased at t<τ and increased at t>τ. This non-equilibrium and non-steady process showed a dynamic scaling behavior in the three-trophic population model.