Competitive aggregation dynamics using phase wave signals

Coupled equations of the phase equation and the equation of cell concentration n are proposed for competitive aggregation dynamics of slime mold in two dimensions. Phase waves are used as tactic signals of aggregation in this model. Several aggregation clusters are formed initially, and target patterns appear around the localized aggregation clusters. Owing to the competition among target patterns, the number of the localized aggregation clusters decreases, and finally one dominant localized pattern survives. If the phase equation is replaced with the complex Ginzburg-Landau equation, several spiral patterns appear, and n is localized near the center of the spiral patterns. After the competition among spiral patterns, one dominant spiral survives.