Consensus of population systems with community structures.
Multicommunity population systems may reach a consensus state where the fractions of each species in different communities agree on a common value. In this paper, by analyzing the evolutionary dynamics based on an extended replicator equation incorporating community effects, the consensus problem of population systems with n communities is studied. In particular, the simple case of two communities is investigated in detail. In general, for n communities, a sufficient and necessary condition for population systems to reach a consensus of coexistent state is provided. Regarding the population dynamics for the four different types of games, whether the population systems can achieve consensus is determined. The dynamics of community-structured populations shows richer features than nonstructured populations, and some nontrivial phenomena arising from different community-structured population systems are illustrated with concrete numerical examples.
Wang
Jing
J
Center for Systems and Control, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China. wj02@pku.edu.cn
Wu
Bin
B
Wang
Long
L
Fu
Feng
F
D000818:Animals; D001717:Birds; D032921:Consensus; D005716:Game Theory; D006801:Humans; D007398:Interpersonal Relations; D008960:Models, Psychological; D011157:Population Dynamics; D044382:Population Groups; D012111:Residence Characteristics; D012919:Social Behavior