Space promotes the coexistence of species: Effective medium approximation for rock-paper-scissors system

作者：Nagatani Takashi; Sato Kazunori; Ichinose Genki; Tainaka Kei ichi^*

来源：Ecological Modelling, 2017, 359: 240-245.

DOI：10.1016/j.ecolmodel.2017.06.001

• Effective medium approximation
• Rock-paper-scissors game
• Stochastic cellular automaton
• Population dynamics
• Self-consistent field
• Spatial pattern formation

Stochastic cellular automata for rock-paper-scissors games are related to Lotka-Volterra model. Simulations are usually performed by two methods local and global interactions. It is well known that the population dynamics with local interaction is stable, where all species coexist. In contrast, global interaction leads to extinction. So far, theories such as mean-field theory and pair approximation have been presented, but they never explained the stable dynamics in local simulation. In the present article, we apply effective medium approximation (EMA) which has been developed in Physics. The effective medium is determined in a self-consistent way. The EMA theory well predicts the stability of population dynamics. Moreover, it fairly explains the aggregation of each species observed in the stationary state.

• 出版日期2017-9-10