噪声对集合种群稳定性的影响

王参军; 李江城; 梅冬成

doi:10.7498/aps.61.120506

摘要

本文在Levins模型的基础上研究了噪声对集合种群的稳定性的影响. 应用Fokker-Planck方程得到了系统的稳态概率分布函数和平均灭绝时间. 经过数值分析,结果如下: 无关联(=0 为加性噪声和乘性噪声之间的关联强度)时, 加性噪声强度和乘性噪声强度D均弱化集合种群的稳定性; 噪声之间关联(0)时, 随着的增大,系统的稳定性被增强. 当-(c-e-D)2/(4cD)1时, 诱导共振抑制现象. D存在一个临界值, 小于临界值时, D可以增强系统的稳定性.

关键词:

集合种群 /
Levins 模型 /
噪声 /
稳定性

Abstract

The Levins model subjected to the noise is employed to study the stability of a metapopulation. The analytic expressions of the stationary probability distribution function and the mean extinction time of the metapopulation are obtained according to the Fokker-Planck Equation. The results show that for the case of no correlation between the additive noise and the multiplicative noise (=0, is the intensity of correlation between multiplicative and additive noise), the increase of the additive noise intensity weakens the stability of a metapopulation; for the case of 0, enhances the stability of a metapopulation. For -(c-e-D)2/(4cD)1, can induce the resonance restrain phenomenon. Meantime, there exists a critical value of D. When D is lower than the critical value, the stability of the system is enhanced.

Keywords:

作者及机构信息

1.
宝鸡文理学院非线性研究所, 宝鸡 721016;

2.
云南大学物理系, 昆明 650091

基金项目: 国家自然科学基金(批准号: 11165016), 陕西省自然科学基金(批准号: 2010JQ1014)和宝鸡文理学院重点科研项目(批准号: ZK11053)资助的课题.

Authors and contacts

1.
Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji 721016, China;

2.
Department of physics, Yunnan University, Kunming 650091, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No.11165016), the Natural Science Foundation of Shaanxi Province, China (Grant No.2010JQ1014), and the Science Foundation of Baoji University of Science and Arts of China (Grant No.ZK11053).

参考文献

[1]	Levins R 1969 Bull. Entomol. Soc. Am. 15 237
[2]	Levins R 1970 Lect. Notes. Math. 2 75
[3]	Gilpin M E, Hanski I 1991 Metapopulation Dynamics:Empirical and Theoretical Investigations (London: Academic Press) p336
[4]	Hanski I, Pakkala T, Kuussaari M, Lei G 1995 Oikos 72 21
[5]	Moilanen A, Hanski I 1998 Ecology 79 2503.
[6]	Hastings A, Harrison S 1994 Ann. Rev. Ecol. Syst. 25 167
[7]	Harrison S 1991 Biol. J. Linn. Soc. 42 73
[8]	Ovaskainen O, Sato K, Bascompte J, Hanski I 2002 J. Theor. Biol. 215 95
[9]	Bascompte J 2001 J. Theor. Biol. 209 373
[10]	Hanski I A 1994 J. Animal Ecol. 63 151
[11]	Jung P, Hänggi P 1989 Europhys. Lett. 8 505
[12]	Jia Y, Zhang X P, Hu X M and Li J R 2001 Phys. Rev. E 63 031107
[13]	Wei X Q, Cao L, Wu D J 1995 Phys. Lett. A 207 338
[14]	Wu D J, Cao L, Ke S Z 1994 Phys. Rev. E 50 2496
[15]	Mei D C, Xie G Z,Cao L, Wu D J 1999 Phys. Rev. E 59 3880
[16]	Mei D C, Xie G Z, Zhang L 2004 Eur. Phys. J. B 41 107
[17]	Ai B Q, Wang X J, Liu G T, Liu L G 2003 Phys. Rev. E 67 22903
[18]	Cai J C, Wang C J, Mei D C 2007 Chin. Phys. Lett. 24 1162
[19]	Wang C J 2012 Acta Phys. Sin. 61 010503 (in Chinese) [王参军 2012 61 010503]
[20]	Wang C J 2012 Acta Phys. Sin. 61 050501 (in Chinese) [王参军 2012 61 050501]
[21]	yJia Y, Li J R 1997 Phys. Rev. Lett. 78 994
[22]	Vilar J M G, Solé R V 1998 Phys. Rev. Lett. 80 4099
[23]	Wang C J, Wei Q, Zheng B B, Mei D C 2008 Acta Phys. Sin. 57 1375(in chinese) [王参军, 魏群, 郑宝兵, 梅冬成 2008 57 1375]
[24]	Zhu S 1993 Phys. Rev. A 47 2405
[25]	Zhang L Y, Cao L, Wu D J 2002 Chin. Phys. 13 353
[26]	Xie C W, Mei D C 2004 Phys. Lett. A 323 421
[27]	Cao L, Wu D J 1999 Phys. Lett. A 260 126
[28]	Li J C, Mei D C 2008 Acta Phys. Sin. 57 (in chinese)6792[李江城, 梅冬成 2008 57 6792]
[29]	Hofbauer J, Sigmund K 1998 Evolutionary Games and Population Dynamics (Cambridge: Cambridge University Press )p91
[30]	May R M 1976 Nature 261 459
[31]	Nie L R, Mei D C 2007 Europhys. Lett. 79 20005
[32]	Li J H, Huang Z Q 1998 Phys. Rev. E 57 3917
[33]	Nie L R, Mei D C 2007 Phys. Lett. A 371 111
[34]	Mei D C, Xie G Z, Cao L and Wu D J 1999 Chin. Phys. Lett. 16 327
[35]	Xie C W, Mei D C 2003 Chin. Phys. Lett. 20 813
[36]	Bak P, Sneppen K 1993 Phys. Rev. Lett. 71 4083
[37]	Ovaskainen O, Hanski I 2001 Theor. Popul. Biol. 60 281
[38]	Lindenberg K, West B J 1986 J. Stat. Phys. 42 201
[39]	Masoliver J, West B J, Lindenberg K 1987 Phys. Rev. A 35 3086

施引文献

[1]	Levins R 1969 Bull. Entomol. Soc. Am. 15 237
[2]	Levins R 1970 Lect. Notes. Math. 2 75
[3]	Gilpin M E, Hanski I 1991 Metapopulation Dynamics:Empirical and Theoretical Investigations (London: Academic Press) p336
[4]	Hanski I, Pakkala T, Kuussaari M, Lei G 1995 Oikos 72 21
[5]	Moilanen A, Hanski I 1998 Ecology 79 2503.
[6]	Hastings A, Harrison S 1994 Ann. Rev. Ecol. Syst. 25 167
[7]	Harrison S 1991 Biol. J. Linn. Soc. 42 73
[8]	Ovaskainen O, Sato K, Bascompte J, Hanski I 2002 J. Theor. Biol. 215 95
[9]	Bascompte J 2001 J. Theor. Biol. 209 373
[10]	Hanski I A 1994 J. Animal Ecol. 63 151
[11]	Jung P, Hänggi P 1989 Europhys. Lett. 8 505
[12]	Jia Y, Zhang X P, Hu X M and Li J R 2001 Phys. Rev. E 63 031107
[13]	Wei X Q, Cao L, Wu D J 1995 Phys. Lett. A 207 338
[14]	Wu D J, Cao L, Ke S Z 1994 Phys. Rev. E 50 2496
[15]	Mei D C, Xie G Z,Cao L, Wu D J 1999 Phys. Rev. E 59 3880
[16]	Mei D C, Xie G Z, Zhang L 2004 Eur. Phys. J. B 41 107
[17]	Ai B Q, Wang X J, Liu G T, Liu L G 2003 Phys. Rev. E 67 22903
[18]	Cai J C, Wang C J, Mei D C 2007 Chin. Phys. Lett. 24 1162
[19]	Wang C J 2012 Acta Phys. Sin. 61 010503 (in Chinese) [王参军 2012 61 010503]
[20]	Wang C J 2012 Acta Phys. Sin. 61 050501 (in Chinese) [王参军 2012 61 050501]
[21]	yJia Y, Li J R 1997 Phys. Rev. Lett. 78 994
[22]	Vilar J M G, Solé R V 1998 Phys. Rev. Lett. 80 4099
[23]	Wang C J, Wei Q, Zheng B B, Mei D C 2008 Acta Phys. Sin. 57 1375(in chinese) [王参军, 魏群, 郑宝兵, 梅冬成 2008 57 1375]
[24]	Zhu S 1993 Phys. Rev. A 47 2405
[25]	Zhang L Y, Cao L, Wu D J 2002 Chin. Phys. 13 353
[26]	Xie C W, Mei D C 2004 Phys. Lett. A 323 421
[27]	Cao L, Wu D J 1999 Phys. Lett. A 260 126
[28]	Li J C, Mei D C 2008 Acta Phys. Sin. 57 (in chinese)6792[李江城, 梅冬成 2008 57 6792]
[29]	Hofbauer J, Sigmund K 1998 Evolutionary Games and Population Dynamics (Cambridge: Cambridge University Press )p91
[30]	May R M 1976 Nature 261 459
[31]	Nie L R, Mei D C 2007 Europhys. Lett. 79 20005
[32]	Li J H, Huang Z Q 1998 Phys. Rev. E 57 3917
[33]	Nie L R, Mei D C 2007 Phys. Lett. A 371 111
[34]	Mei D C, Xie G Z, Cao L and Wu D J 1999 Chin. Phys. Lett. 16 327
[35]	Xie C W, Mei D C 2003 Chin. Phys. Lett. 20 813
[36]	Bak P, Sneppen K 1993 Phys. Rev. Lett. 71 4083
[37]	Ovaskainen O, Hanski I 2001 Theor. Popul. Biol. 60 281
[38]	Lindenberg K, West B J 1986 J. Stat. Phys. 42 201
[39]	Masoliver J, West B J, Lindenberg K 1987 Phys. Rev. A 35 3086

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