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

Abstract

We propose an aggregation evolution model of two-species (A- and B-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) = J2k, and meanwhile the interaction between the aggregates of different species 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 the two self-birth processes, and the initial monomer concentrations A0 and B0 play important roles, while the lose-lose scheme play important roles in some special cases.