Coevolutionary dynamics with clustering behaviors on cyclic competition

We propose a dynamic model for describing clustering behaviors on a cyclic game, in which the same species form a cluster to compete. The rates of consuming the prey depend not only on the individual competing ability v$v$, but also on the two interacting cluster’s sizes. The fragmentation and coagulation rates of the clusters are related to the cohesive strength among the individuals. A new parameter u$u$ is introduced to indicate the uniting degree. We find that the probability distribution of the clustering sizes is almost a power law in a large regime specified by the two parameters, which reflects the scale-free behavior in complex systems. In addition, the exponential magnitudes are mostly in the range of real social systems. Our simulation shows that clustering promotes biodiversity. At steady state, the amounts about the three species evolve tempestuously with asymmetric period; the aggregations about big size’s clusters to compete are obvious and on–off intermittence.