The process of coevolutionary competitive exclusion: speciation, multifractality and power-laws in correlation

Competitive exclusion, a key principle of ecology, can be generalized to understand many other complex systems. Individuals under surviving pressure tend to be different from others, and correlations among them change correspondingly to the updating of their states. We show with numerical simulation that these aptitudes can contribute to group formation or speciation in social fields. Moreover, they can lead to power-law topological correlations of complex networks. By coupling updating states of nodes with variation of connections in a network, structural properties with power-laws and functions like multifractality, spontaneous ranking and evolutionary branching of node states can emerge out simultaneously from the present self-organized model of coevolutionary process.

💡 Research Summary

The paper extends the ecological principle of competitive exclusion to the domain of complex adaptive systems by constructing a co‑evolutionary network model in which node states and link weights are updated simultaneously. Each node i carries a continuous scalar variable x_i(t) that represents its internal “state” (e.g., opinion, fitness, or strategy). At each discrete time step the state is nudged toward the average of its neighbors: Δx_i = ε