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Monostable waves and spreading speed for a reaction-diffusion model with seasonal succession
1. | Department of Mathematics, School of Science, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China |
2. | Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7 |
References:
[1] |
P. J. DuBowy, Waterfowl communities and seasonal environments: Temporal variabolity in interspecific competition, Ecology, 69 (1988), 1439-1453.
doi: 10.2307/1941641. |
[2] |
J. Fang and X.-Q. Zhao, Travelling waves for monotone semiflows with weak compactness, SIAM J. Math. Anal., 46 (2014), 3678-3704.
doi: 10.1137/140953939. |
[3] |
S. Gourley, R. Liu and J. Wu, Spatiotemporal distributions of migratory birds: Patchy models with delay, SIAM J. Appl. Dyn. Syst., 9 (2010), 589-610.
doi: 10.1137/090767261. |
[4] |
S.-B. Hsu and X.-Q. Zhao, A Lotka-Volterra competition model with seasonal succession, J. Math. Biol., 64 (2012), 109-130.
doi: 10.1007/s00285-011-0408-6. |
[5] |
S. S. Hu and A. J. Tessier, Seasonal succession and the strength of intra- and interspecific competition in a Daphnia assemblage, Ecology, 76 (1995), 2278-2294.
doi: 10.2307/1941702. |
[6] |
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speed and linear determinacy for two-species competition models, J. Math. Biol., 45 (2002), 219-233.
doi: 10.1007/s002850200144. |
[7] |
X. Liang, Y. Yi and X.-Q. Zhao, Spreading speeds and travelling waves for periodic evolution systems, J. Differential Equations, 231 (2006), 57-77.
doi: 10.1016/j.jde.2006.04.010. |
[8] |
X. Liang and X.-Q. Zhao, Asymptotic speeds of speed and travelling waves for monotone semiflows with application, Comm. Pure Appl. Math., 60 (2007), 1-40.
doi: 10.1002/cpa.20154. |
[9] |
E. Litchman and C. A. Klausmeier, Competition of phytoplankton under fluctuating light, Amer. Naturalist, 157 (2001), 170-187.
doi: 10.1086/318628. |
[10] |
R. Peng and X.-Q. Zhao, The diffusive logistic model with a free boundary and seasonal succession, Discrete. Contin. Dyn. Syst. (Ser. A), 33 (2013), 2007-2031.
doi: 10.3934/dcds.2013.33.2007. |
[11] |
C. F. Steiner, A. S. Schwaderer, V. Huber, C. A. Klausmeier and E. Litchman, Periodically forced food chain dynamics: Model predictions and experimental validation, Ecology, 90 (2009), 3099-3107.
doi: 10.1890/08-2377.1. |
[12] |
H. F. Weinberger, M. A. Lewis and B. Li, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol., 45 (2002), 183-218.
doi: 10.1007/s002850200145. |
[13] |
F. Zhang and X.-Q. Zhao, A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007), 496-516.
doi: 10.1016/j.jmaa.2006.01.085. |
[14] |
Y. Zhang and X.-Q. Zhao, Bistable travelling waves for a reaction and diffusion model with seasonal succession, Nonlinearity, 26 (2013), 691-709.
doi: 10.1088/0951-7715/26/3/691. |
show all references
References:
[1] |
P. J. DuBowy, Waterfowl communities and seasonal environments: Temporal variabolity in interspecific competition, Ecology, 69 (1988), 1439-1453.
doi: 10.2307/1941641. |
[2] |
J. Fang and X.-Q. Zhao, Travelling waves for monotone semiflows with weak compactness, SIAM J. Math. Anal., 46 (2014), 3678-3704.
doi: 10.1137/140953939. |
[3] |
S. Gourley, R. Liu and J. Wu, Spatiotemporal distributions of migratory birds: Patchy models with delay, SIAM J. Appl. Dyn. Syst., 9 (2010), 589-610.
doi: 10.1137/090767261. |
[4] |
S.-B. Hsu and X.-Q. Zhao, A Lotka-Volterra competition model with seasonal succession, J. Math. Biol., 64 (2012), 109-130.
doi: 10.1007/s00285-011-0408-6. |
[5] |
S. S. Hu and A. J. Tessier, Seasonal succession and the strength of intra- and interspecific competition in a Daphnia assemblage, Ecology, 76 (1995), 2278-2294.
doi: 10.2307/1941702. |
[6] |
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speed and linear determinacy for two-species competition models, J. Math. Biol., 45 (2002), 219-233.
doi: 10.1007/s002850200144. |
[7] |
X. Liang, Y. Yi and X.-Q. Zhao, Spreading speeds and travelling waves for periodic evolution systems, J. Differential Equations, 231 (2006), 57-77.
doi: 10.1016/j.jde.2006.04.010. |
[8] |
X. Liang and X.-Q. Zhao, Asymptotic speeds of speed and travelling waves for monotone semiflows with application, Comm. Pure Appl. Math., 60 (2007), 1-40.
doi: 10.1002/cpa.20154. |
[9] |
E. Litchman and C. A. Klausmeier, Competition of phytoplankton under fluctuating light, Amer. Naturalist, 157 (2001), 170-187.
doi: 10.1086/318628. |
[10] |
R. Peng and X.-Q. Zhao, The diffusive logistic model with a free boundary and seasonal succession, Discrete. Contin. Dyn. Syst. (Ser. A), 33 (2013), 2007-2031.
doi: 10.3934/dcds.2013.33.2007. |
[11] |
C. F. Steiner, A. S. Schwaderer, V. Huber, C. A. Klausmeier and E. Litchman, Periodically forced food chain dynamics: Model predictions and experimental validation, Ecology, 90 (2009), 3099-3107.
doi: 10.1890/08-2377.1. |
[12] |
H. F. Weinberger, M. A. Lewis and B. Li, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol., 45 (2002), 183-218.
doi: 10.1007/s002850200145. |
[13] |
F. Zhang and X.-Q. Zhao, A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007), 496-516.
doi: 10.1016/j.jmaa.2006.01.085. |
[14] |
Y. Zhang and X.-Q. Zhao, Bistable travelling waves for a reaction and diffusion model with seasonal succession, Nonlinearity, 26 (2013), 691-709.
doi: 10.1088/0951-7715/26/3/691. |
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