Cyclical game coupling with Levy flight and Brownian motion and stable coexistence conditions of species

Wang Dong; Tang Chang-Qing; Tian Bao-Guo; Qu Liang-Sheng; Zhang Jin-Chun; Di Zeng-Ru

doi:10.7498/aps.63.168701

Abstract

Cyclical game is often used to study the biodiversity in ecosystem. However, the interaction distance mode considered in previous studies of cyclical game is only the interaction between nearest neighbors, a fixed distance, or a random value of fixed distance among the individuals of species. This is not consistent with the actual situation. In this paper, considering the fact that Levy flight and Brownian motion widespreadly exist in ecosystem, and comprehensively considering the nearest-neighbor-interaction and long-range-interaction given by Levy flight and Brownian motion, the cyclical game and conditions of maintaining biodiversity are investigated. The critical relation of maximal step length of flight versus choosing probability is presented, including Logistic and exponent relations. Further the critical relation between power-law exponent and choosing probability is found. The condition of maintaining species coexistence is also found.

Keywords:

Authors and contacts

1.
Department of Basic Science, Naval Aeronautical and Astronautical University, Yantai 264001, China;
2.
School of Systems Science, Beijing Normal University, Beijing 100875, China;
3.
Administrant Brigade of Postgraduate, Naval Aeronautical and Astronautical University, Yantai 264001, China
Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61174150, 60974084) and the Program for the New Century Excellent Talents in University of Ministry of Education, China (Grant No. NCET-09-0228).

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Cited By

[1]	Sinervo B, Lively C M 1996 Nature 380 240
[2]	Kerr B, Riley M A, Feldman M W, Bohannan B J M 2002 Nature 418 171
[3]	Kirkup B C, Riley M A 2004 Nature 428 412
[4]	Jackson J B C, Buss L 1975 Proc. Natl. Acad. Sci. USA 72 5160
[5]	Paquin C E, Adams J 1983 Nature 306 368
[6]	Gilg O, Hanski I, Sittler B 2003 Science 302 866
[7]	Reichenbach T, Mobilia M, Frey E 2007 Nature 448 1046
[8]	Reichenbach T, Mobilia M, Frey E 2007 Phys. Rev. Lett. 99 238105
[9]	Reichenbach T, Mobilia M, Frey E 2008 J. Theor. Biol. 254 368
[10]	Reichenbach T, Frey E 2008 Phys. Rev. Lett. 101 058102
[11]	Wang W M, Wang W J, Lin Y Z, Tan Y J 2011 Chin. Phys. B 20 034702
[12]	Quan J, Wang X J 2011 Chin. Phys. B 20 030203
[13]	Ying C Y, Hua D Y, Wang L Y 2007 J. Phys. A: Math. Theor. 40 4477
[14]	Sun R S, Hua D Y 2009 Chin. Phys. Lett. 26 086403
[15]	Hua D Y, Dai L C, Lin C 2013 Europhys. Lett. 101 38004
[16]	Zhang G Y, Chen Y, Qi W K, Qing S M 2009 Phys. Rev. E 79 062901
[17]	Szabo G, Fath G 2007 Phys. Rep. 446 97
[18]	Shi H J, Wang W X, Yang R, Lai Y C 2010 Phys. Rev. E 81 030901R
[19]	Ni X, Wang W X, Lai Y C, Grebogi C 2010 Phys. Rev. E 82 066211
[20]	Wang W X, Ni X, Lai Y C, Grebogi C 2011 Phys. Rev. E 83 11917
[21]	Nossal R 1983 J. Stat. Phys. 30 391
[22]	Viswanathan G M, Afanasyev V, Buldyrev S V, Murphy E J, Prince P A, Stanley H E 1996 Nature 381 413
[23]	Levandowsky M, White B S, Schuster F L 1997 Acta Protozool. 36 237
[24]	Ramos F G, Mateos J L, Miramontes O, Cocho G, Larralde H, Ayala O B 2004 Behav. Ecol. Sociobiol. 55 223
[25]	Dieterich P, Klages R, Preuss R, Schwab A 2008 Proc. Natl. Acad. Sci. USA 105 459
[26]	Humphries N E, Queiroz N, Dyer J R M, Pade N G, Musyl M K, Schaefer K M, Fuller D W, Brunnschweiler J M, Doyle T K, Houghton J D R, Hays G C, Jones C S, Noble L R, Wearmouth V J, Southall E J, Sims D W 2010 Nature 465 1066
[27]	Viswanathan G M, Raposo E P, da Luz M G E 2008 Phys. Life Rev. 5 133
[28]	Bartumeus F, Peters F, Pueyo S, Marrase C, Catalan J 2003 Proc. Natl. Acad. Sci. USA 100 12771
[29]	Bartumeus F 2007 Fractals 15 151
[30]	Sims D W, Southall E J, Humphries N E, Hays G C, Bradshaw C J A, Pitchford J W, James A, Ahmed M Z, Brierley A S, Hindell M A, Morritt D, Musyl M K, Righton D, Shepard E L C, Wearmouth V J, Wilson R P, Witt M J, Metcalfe J D 2008 Nature 451 1098
[31]	Sims D W, Righton D, Pitchford J W 2007 J. Anim. Ecol. 76 222
[32]	Travis J 2007 Science 318 742
[33]	Buchanan M 2008 Nature 453 714
[34]	Wang D, Zhuang Q, Fan Y, Di Z R 2013 Chin. Phys. B 22 128702
[35]	Gillespie D T 1976 J. Comput. Phys. 22 403
[36]	Gillespie D T 1977 J. Phys. Chem. 81 2340
[37]	Hastings A, Petrovskii S, Morozov A 2011 Biol. Lett. 7 163
[38]	Metzler R, Klafter J 2000 Phys. Rep. 339 1

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Vol. 63, Issue 16 - 2014-08-20

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