August  2013, 33(8): 3443-3472. doi: 10.3934/dcds.2013.33.3443

Spreading speeds of $N$-season spatially periodic integro-difference models

1. 

Wu Wen-Tsun Key Laboratory of Mathematics and School of Mathematical Science, University of Science and Technology of China, Hefei, Anhui 230026, China, China, China

Received  May 2012 Revised  August 2012 Published  January 2013

In this paper, the spreading speeds of $N$-season spatially periodic integro-difference models are investigated. The variational formula of the spreading speeds is given via the principal eigenvalues of the respective positive linear operators. The effects of the spatial and temporal distribution of the intrinsic growth rates on the spreading speeds are considered.
Citation: Weiwei Ding, Xing Liang, Bin Xu. Spreading speeds of $N$-season spatially periodic integro-difference models. Discrete & Continuous Dynamical Systems, 2013, 33 (8) : 3443-3472. doi: 10.3934/dcds.2013.33.3443
References:
[1]

J. Func. Anal., 255 (2008), 2146-2189. doi: 10.1016/j.jfa.2008.06.030.  Google Scholar

[2]

J. Eur. Math. Soc., 7 (2005), 173-213. doi: 10.4171/JEMS/26.  Google Scholar

[3]

J. Math. Pures Appl. (9), 84 (2005), 1101-1146. doi: 10.1016/j.matpur.2004.10.006.  Google Scholar

[4]

Disc. Cont. Dyn. Systems, 25 (2009), 321-342. doi: 10.3934/dcds.2009.25.321.  Google Scholar

[5]

in "Stochastic Analysis and Applications" (ed. M. Pinsky), Adv. Prob. Rel. Topics, Vol. 7, Dekker, New York, (1984), 147-166.  Google Scholar

[6]

Sov. Math. Dokl., 20 (1979), 1282-1286. Google Scholar

[7]

Math. Ann., 335 (2006), 489-525. doi: 10.1007/s00208-005-0729-0.  Google Scholar

[8]

Indiana Univ. Math. J., to appear, (2010). Google Scholar

[9]

Bull. Math. Biol., 72 (2010), 1166-1191. doi: 10.1007/s11538-009-9486-7.  Google Scholar

[10]

G. Hetzer, W. Shen and A. Zhang, Effects of spatial variations and dispersal strategies on principal eigenvalues of dispersal operators and spreading speeds of monostable equations,, Rocky Mountain Journal of Mathematics, ().   Google Scholar

[11]

SIAM J. Math. Anal., 40 (2008), 776-789. doi: 10.1137/070703016.  Google Scholar

[12]

J. Dyn. Diff. Equat., 21 (2009), 501-525. doi: 10.1007/s10884-009-9138-5.  Google Scholar

[13]

Ecology, 77 (1996), 2027-2042. Google Scholar

[14]

Japan J. Indust. Appl. Math., 34 (2007), 3-15.  Google Scholar

[15]

Math. Biosci., 93 (1989), 269-295. doi: 10.1016/0025-5564(89)90026-6.  Google Scholar

[16]

Trans. Am. Math. Soc., 362 (2010), 5605-5633. doi: 10.1090/S0002-9947-2010-04931-1.  Google Scholar

[17]

Comm. Pure Appl. Math., 60 (2007), 1-40. doi: 10.1002/cpa.20154.  Google Scholar

[18]

J. Funct. Anal., 259 (2010), 857-903. doi: 10.1016/j.jfa.2010.04.018.  Google Scholar

[19]

SIAM J. Math. Anal., 4 (2009), 2388-2406. doi: 10.1137/080743597.  Google Scholar

[20]

Ann. Mat. Pura Appl., 188 (2009), 269-295. doi: 10.1007/s10231-008-0075-4.  Google Scholar

[21]

European J. Appl. Math., 22 (2011), 169-185. doi: 10.1017/S0956792511000027.  Google Scholar

[22]

J. Fisheries Research Board of Canada, 11 (1954), 559-623. Google Scholar

[23]

Commun. Math. Sci., 5 (2007), 575-593.  Google Scholar

[24]

Trans. Amer. Math. Soc., 362 (2010), 5125-5168. doi: 10.1090/S0002-9947-10-04950-0.  Google Scholar

[25]

Oxford University Press, 1997. Google Scholar

[26]

Theor. Popul. Biol., 30 (1986), 143-160. doi: 10.1016/0040-5809(86)90029-8.  Google Scholar

[27]

J. Differential Equations, 249 (2010), 747-795. doi: 10.1016/j.jde.2010.04.012.  Google Scholar

[28]

J. Math. Biol., 8 (1979), 173-187. doi: 10.1007/BF00279720.  Google Scholar

[29]

J. Math. Biol., 45 (2002), 511-548. doi: 10.1007/s00285-002-0169-3.  Google Scholar

[30]

SIAM J. Math. Anal., 13 (1982), 353-396. doi: 10.1137/0513028.  Google Scholar

[31]

J. Math. Biol., 57 (2008), 387-411. doi: 10.1007/s00285-008-0168-0.  Google Scholar

[32]

SIAM Rev., 42 (2000), 161-230. doi: 10.1137/S0036144599364296.  Google Scholar

[33]

Arch. Ration. Mech. Anal., 195 (2009), 441-453. doi: 10.1007/s00205-009-0282-1.  Google Scholar

show all references

References:
[1]

J. Func. Anal., 255 (2008), 2146-2189. doi: 10.1016/j.jfa.2008.06.030.  Google Scholar

[2]

J. Eur. Math. Soc., 7 (2005), 173-213. doi: 10.4171/JEMS/26.  Google Scholar

[3]

J. Math. Pures Appl. (9), 84 (2005), 1101-1146. doi: 10.1016/j.matpur.2004.10.006.  Google Scholar

[4]

Disc. Cont. Dyn. Systems, 25 (2009), 321-342. doi: 10.3934/dcds.2009.25.321.  Google Scholar

[5]

in "Stochastic Analysis and Applications" (ed. M. Pinsky), Adv. Prob. Rel. Topics, Vol. 7, Dekker, New York, (1984), 147-166.  Google Scholar

[6]

Sov. Math. Dokl., 20 (1979), 1282-1286. Google Scholar

[7]

Math. Ann., 335 (2006), 489-525. doi: 10.1007/s00208-005-0729-0.  Google Scholar

[8]

Indiana Univ. Math. J., to appear, (2010). Google Scholar

[9]

Bull. Math. Biol., 72 (2010), 1166-1191. doi: 10.1007/s11538-009-9486-7.  Google Scholar

[10]

G. Hetzer, W. Shen and A. Zhang, Effects of spatial variations and dispersal strategies on principal eigenvalues of dispersal operators and spreading speeds of monostable equations,, Rocky Mountain Journal of Mathematics, ().   Google Scholar

[11]

SIAM J. Math. Anal., 40 (2008), 776-789. doi: 10.1137/070703016.  Google Scholar

[12]

J. Dyn. Diff. Equat., 21 (2009), 501-525. doi: 10.1007/s10884-009-9138-5.  Google Scholar

[13]

Ecology, 77 (1996), 2027-2042. Google Scholar

[14]

Japan J. Indust. Appl. Math., 34 (2007), 3-15.  Google Scholar

[15]

Math. Biosci., 93 (1989), 269-295. doi: 10.1016/0025-5564(89)90026-6.  Google Scholar

[16]

Trans. Am. Math. Soc., 362 (2010), 5605-5633. doi: 10.1090/S0002-9947-2010-04931-1.  Google Scholar

[17]

Comm. Pure Appl. Math., 60 (2007), 1-40. doi: 10.1002/cpa.20154.  Google Scholar

[18]

J. Funct. Anal., 259 (2010), 857-903. doi: 10.1016/j.jfa.2010.04.018.  Google Scholar

[19]

SIAM J. Math. Anal., 4 (2009), 2388-2406. doi: 10.1137/080743597.  Google Scholar

[20]

Ann. Mat. Pura Appl., 188 (2009), 269-295. doi: 10.1007/s10231-008-0075-4.  Google Scholar

[21]

European J. Appl. Math., 22 (2011), 169-185. doi: 10.1017/S0956792511000027.  Google Scholar

[22]

J. Fisheries Research Board of Canada, 11 (1954), 559-623. Google Scholar

[23]

Commun. Math. Sci., 5 (2007), 575-593.  Google Scholar

[24]

Trans. Amer. Math. Soc., 362 (2010), 5125-5168. doi: 10.1090/S0002-9947-10-04950-0.  Google Scholar

[25]

Oxford University Press, 1997. Google Scholar

[26]

Theor. Popul. Biol., 30 (1986), 143-160. doi: 10.1016/0040-5809(86)90029-8.  Google Scholar

[27]

J. Differential Equations, 249 (2010), 747-795. doi: 10.1016/j.jde.2010.04.012.  Google Scholar

[28]

J. Math. Biol., 8 (1979), 173-187. doi: 10.1007/BF00279720.  Google Scholar

[29]

J. Math. Biol., 45 (2002), 511-548. doi: 10.1007/s00285-002-0169-3.  Google Scholar

[30]

SIAM J. Math. Anal., 13 (1982), 353-396. doi: 10.1137/0513028.  Google Scholar

[31]

J. Math. Biol., 57 (2008), 387-411. doi: 10.1007/s00285-008-0168-0.  Google Scholar

[32]

SIAM Rev., 42 (2000), 161-230. doi: 10.1137/S0036144599364296.  Google Scholar

[33]

Arch. Ration. Mech. Anal., 195 (2009), 441-453. doi: 10.1007/s00205-009-0282-1.  Google Scholar

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