Species diversity in rock–paper–scissors game coupling with Levy flight

doi:10.1088/1674-1056/22/12/128702

Abstract The rock–paper–scissors (RPS) game is a nice model to study the biodiversity in an ecosystem. However, in the previous studies only the nearest-neighbor interaction among the species was considered. In this paper, taking the long-range migration into account, the effects of the interplay between nearest-neighbor-interaction and long-range-interaction given by Levy flight with distance distribution l^h (-3 ≤ h <-1) in the spatial RPS game are investigated. Taking the probability, exchange rate, and power-law exponent of Levy flight as parameters, the coexistence conditions of three species are given. The critical curves for stable coexistence of three species in the parameter space are presented. It is also found that Levy flight has interesting effects on the final spatiotemporal pattern of the system. The results reveal that the long-range-interaction given by Levy flight exhibits pronounced effects on biodiversity of the ecosystem.

Keywords: RPS game Levy flight biodiversity spatial pattern

Received: 04 May 2013
Revised: 18 July 2013
Accepted manuscript online:

PACS:	87.23.Cc	(Population dynamics and ecological pattern formation)
	89.75.Da	(Systems obeying scaling laws)
	89.75.Kd	(Patterns)

Fund: Project partially supported by the National Natural Science Foundation of China (Grant Nos. 61174150 and 60974084), the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-09-0228), the Fundamental Research Funds for the Central Universities of Beijing Normal University, and the High Performance Computing Center of Beijing Normal University.

Corresponding Authors: Di Zeng-Ru
E-mail: zdi@bnu.edu.cn

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Wang Dong (王栋), Zhuang Qian (庄倩), Fan Ying (樊瑛), Di Zeng-Ru (狄增如) Species diversity in rock–paper–scissors game coupling with Levy flight 2013 Chin. Phys. B 22 128702

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Species diversity in rock–paper–scissors game coupling with Levy flight

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