title: Consensus of population systems with community structures.
abstract: 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.
authors.affiliation: 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
authors.forename: Jing
authors.initials: J
authors.lastname: Wang
authors.forename: Bin
authors.initials: B
authors.lastname: Wu
authors.forename: Long
authors.initials: L
authors.lastname: Wang
authors.forename: Feng
authors.initials: F
authors.lastname: Fu
mesh_terms: 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