Aggregation Behaviors of a Two-Species System with Lose-Lose Interactions

We propose an aggregation evolution model of two-species (A- andB-species) aggregates to study the prevalent aggregation phenomena in social and economic systems. In this model, A- and B-species aggregates perform self-exchange-driven growths with the exchange rate kernels K(k,l)=Kkl and L(k,l)=Lkl, respectively, and the two species aggregates perform self-birth processes with the rate kernels J₁(k)=J₁k and J₂(k)=J₂2k,and meanwhile the interaction between the aggregates of differentspecies A and B causes a lose-lose scheme with the rate kernel H(k,l)=Hkl. Based on the mean-field theory, we investigated the evolution behaviors of the two species aggregates to study the competitions among above three aggregate evolution schemes on the distinct initial monomer concentrations A₀ and B₀ of the two species. The results show that the evolution behaviors of A- and B-species are crucially dominated by the competition between thetwo self-birth processes, and the initial monomer concentrationsA₀ and B₀ play important roles, while the lose-lose scheme play important roles in some special cases.