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

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

中国物理B ›› 2013, Vol. 22 ›› Issue (12): 128702-128702.doi: 10.1088/1674-1056/22/12/128702

• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇下一篇

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

王栋^{a b}, 庄倩^b, 樊瑛^b, 狄增如^b

a Department of Basic Science, Naval Aeronautical and Astronautical University, Yantai 264001, China;
b School of Systems Science and Center for Complexity Research, Beijing Normal University, Beijing 100875, China

收稿日期:2013-05-04 修回日期:2013-07-18 出版日期:2013-10-25 发布日期:2013-10-25
基金资助:
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.

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

Wang Dong (王栋)^{a b}, Zhuang Qian (庄倩)^b, Fan Ying (樊瑛)^b, Di Zeng-Ru (狄增如)^b

a Department of Basic Science, Naval Aeronautical and Astronautical University, Yantai 264001, China;
b School of Systems Science and Center for Complexity Research, Beijing Normal University, Beijing 100875, China

Received:2013-05-04 Revised:2013-07-18 Online:2013-10-25 Published:2013-10-25
Contact: Di Zeng-Ru E-mail:zdi@bnu.edu.cn
Supported by:
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.

摘要/Abstract

摘要： 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.

关键词: RPS game, Levy flight, biodiversity, spatial pattern

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.

Key words: RPS game, Levy flight, biodiversity, spatial pattern

中图分类号: (Population dynamics and ecological pattern formation)

87.23.Cc

89.75.Da (Systems obeying scaling laws) 89.75.Kd (Patterns)

王栋, 庄倩, 樊瑛, 狄增如. Species diversity in rock–paper–scissors game coupling with Levy flight[J]. 中国物理B, 2013, 22(12): 128702-128702.

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[J]. Chin. Phys. B, 2013, 22(12): 128702-128702.

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

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

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