1. Space promotes the coexistence of species: Effective medium approximation for rock-paper-scissors system
- Author
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Genki Ichinose, Takashi Nagatani, Kei-ichi Tainaka, and Kazunori Sato
- Subjects
0106 biological sciences ,education.field_of_study ,Pair approximation ,Extinction ,Ecological Modeling ,Population ,Space (mathematics) ,Spatial pattern formation ,01 natural sciences ,Stability (probability) ,010601 ecology ,Stochastic cellular automaton ,0103 physical sciences ,Quantitative Biology::Populations and Evolution ,Statistical physics ,010306 general physics ,education ,Mathematical economics ,Stationary state ,Mathematics - Abstract
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.
- Published
- 2017
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