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In this paper, the stability for a metapopulation system driven by colored cross-correlated noises is investigated based on the Levins model. The stationary probability distribution and the explicit expression of the mean extinction time are derived according to the Fokker-Planck equation. Numerical results show that in the case of colored correlation between two noises, the addictive noise and the multiplicative noise intensity weaken the stability of metapopulation, and the correlation strength enhances the stability of metapopulation. If the correlation strength between the two noises is negative, the mean extinction time is a decreasing function of intensities of the two noises, but a increasing function of correlation time; if the correlation strength between the two noises is positive, then the mean extinction time is a decreasing function of addictive noise intensity and correlation time, but a non-monotonic function of multiplicative noise intensity.
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Keywords:
- metapopulation /
- colored cross-correlated noises /
- stability /
- mean extinction time
[1] Levins R 1998 Bull. Entomol. Soc. Am. 15 237
[2] Levins R 1970 Lect. Notes. Math. 2 75
[3] Gilpin M E, Hanski I 1991 Metapopulation Dynamics (London Academic Press) p366
[4] Hanski I, Pakkala T, Kuussaari M 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] Jia Y, Zhang X P, Hu X M, Li J R 2001 Phys. Rev. E 63 031107
[9] Wei X Q, Cao L, Wu D J 1995 Phys. Lett. A 207 338
[10] Mei D C, Xie G Z, Cao L, Wu D J 1999 Phys. Rev. E 59 3880
[11] Wang C J 2012 Acta Phys. Sin. 61 010503 (in Chinese) [王参军 2012 物理学报 61 010503]
[12] Wang C J, Li J C, Mei D C 2012 Acta Phys. Sin. 61 120506 (in Chinese) [王参军, 李江成, 梅冬成 2012 物理学报 61 120506]
[13] Ai B Q, Wang X J, Liu G T, Liu L G 2003 Phys. Rev. E 67 22903
[14] Cai J C, Wang C J, Mei D C 2007 Chin. Phys. Lett. 24 1162
[15] Mei D C, Xie G Z, Zhang L 2004 Eur. Phys. Lett. B 41 107
[16] Jia Y, Li J R 1997 Phys. Rev. Lett. 78 994
[17] Yang J H, Liu X B 2010 Acta Phys. Sin. 59 3727 (in Chinese) [杨建华, 刘先斌 2010 物理学报 59 3727]
[18] Zhang L Y, Cao L, Wu D J 2002 Chin. Phys. Lett. 11 353
[19] Cao L, Wu D J 1999 Phys. Lett. A 260 127
[20] Li J C, Mei D C 2008 Acta Phys. Sin. 57 6792 (in Chinese) [李江成, 梅冬成 2008 物理学报 57 6792]
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[1] Levins R 1998 Bull. Entomol. Soc. Am. 15 237
[2] Levins R 1970 Lect. Notes. Math. 2 75
[3] Gilpin M E, Hanski I 1991 Metapopulation Dynamics (London Academic Press) p366
[4] Hanski I, Pakkala T, Kuussaari M 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] Jia Y, Zhang X P, Hu X M, Li J R 2001 Phys. Rev. E 63 031107
[9] Wei X Q, Cao L, Wu D J 1995 Phys. Lett. A 207 338
[10] Mei D C, Xie G Z, Cao L, Wu D J 1999 Phys. Rev. E 59 3880
[11] Wang C J 2012 Acta Phys. Sin. 61 010503 (in Chinese) [王参军 2012 物理学报 61 010503]
[12] Wang C J, Li J C, Mei D C 2012 Acta Phys. Sin. 61 120506 (in Chinese) [王参军, 李江成, 梅冬成 2012 物理学报 61 120506]
[13] Ai B Q, Wang X J, Liu G T, Liu L G 2003 Phys. Rev. E 67 22903
[14] Cai J C, Wang C J, Mei D C 2007 Chin. Phys. Lett. 24 1162
[15] Mei D C, Xie G Z, Zhang L 2004 Eur. Phys. Lett. B 41 107
[16] Jia Y, Li J R 1997 Phys. Rev. Lett. 78 994
[17] Yang J H, Liu X B 2010 Acta Phys. Sin. 59 3727 (in Chinese) [杨建华, 刘先斌 2010 物理学报 59 3727]
[18] Zhang L Y, Cao L, Wu D J 2002 Chin. Phys. Lett. 11 353
[19] Cao L, Wu D J 1999 Phys. Lett. A 260 127
[20] Li J C, Mei D C 2008 Acta Phys. Sin. 57 6792 (in Chinese) [李江成, 梅冬成 2008 物理学报 57 6792]
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