1202.2951 (Dong Wang et al.)

Species Diversity in Rock-Paper-Scissors Game Coupling with Levy Flight    [PDF]

Dong Wang, Qian Zhuang, Jing Zhang, Zengru Di

Rock-paper-scissors (RPS) game is a nice model to study the biodiversity in
ecosystem. However, the previous studies only consider the nearest- neighbor-
interaction among the species. In this paper, taking the long range migration
into account, the effects of the interplay between nearest-neighbor-interaction
and long-range-interaction of Levy flight obey the power law distance
distribution with the exponent h (-0.3investigated. Taking the probability of long range Levy flight and the power
exponent as parameters, the coexistence conditions of three species are found.
The critical curves for stable coexistence of three species in the parameters
space are presented. It is also found that long-range-interaction with Levy
flight has interesting effects on the final spatiotemporal pattern of the
system. The results reveal that the long-range-interaction of Levy flight
exhibit pronounced effects on biodiversity of ecosystem.

View original: http://arxiv.org/abs/1202.2951