Citation: |
[1] |
D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in "Partial Differential Equations and Related Topics" Lecture Notes in Math., 446, Springer, Berlin, (1975), 5-49. |
[2] |
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusions arising in population genetics, Adv. Math., 30 (1978), 33-76.doi: 10.1016/0001-8708(78)90130-5. |
[3] |
G. Bunting, Y. Du and K. Krakowski, Spreading speed revisited: Analysis of a free boundary model, Networks and Heterogeneous Media, to appear. |
[4] |
X. F. Chen and A. Friedman, A free boundary problem arising in a model of wound healing, SIAM J. Math. Anal., 32 (2000), 778-800.doi: 10.1137/S0036141099351693. |
[5] |
D. L. DeAngelis, J. C. Trexler and D. D. Donalson, "Competition Dynamics in a Seasionally Varying Wetland," Chapter 1, 1-13, in "Spatial Ecology" (Eds. S. Cantrell, C. Cosner and S. Ruan), CRC Press, Chapman and Hall, (2009). |
[6] |
Y. Du and Z. M. Guo, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary II, J. Differential Equations, 250 (2011), 4336-4366.doi: 10.1016/j.jde.2011.02.011. |
[7] |
Y. Du, Z. M. Guo and R. Peng, A diffusive logistic model with a free boundary in time-periodic environment, preprint, 2011. |
[8] |
Y. Du and Z. G. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377-405.doi: 10.1137/090771089. |
[9] |
P. J. DuBowy, Waterfowl communities and seasonal environments: Temporal variabolity in interspecific competition, Ecology, 69 (1988), 1439-1453. |
[10] |
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. |
[11] |
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. |
[12] |
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Amer. Math. Soc. Providence, RI, 1968. |
[13] |
X. Liang, Y. Yi and X.-Q. Zhao, Spreading speeds and traveling waves for periodic evolution systems, J. Differential Equations, 231 (2006), 57-77.doi: 10.1016/j.jde.2006.04.010. |
[14] |
X. Liang and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 60 (2007), 1-40.doi: 10.1002/cpa.20154. |
[15] |
Z. G. Lin, A free boundary problem for a predator-prey model, Nonlinearity, 20 (2007), 1883-1892.doi: 10.1088/0951-7715/20/8/004. |
[16] |
E. Litchman and C. A. Klausmeier, Competition of phytoplankton under fluctuating light, American Naturalist, 157 (2001), 170-187. |
[17] |
T. R. Malthus, "An Essay on the Principle of Population," 1798. Printed for J. Johnson in St. Pauls Church-Yard, 1998. |
[18] |
M. Mimura, Y. Yamada and S. Yotsutani, A free boundary problem in ecology, Japan J. Appl. Math., 2 (1985), 151-186.doi: 10.1007/BF03167042. |
[19] |
G. Nadin, The principal eigenvalue of a space-time periodic parabolic operator, Ann. Mat. Pura Appl., 188 (2009), 269-295.doi: 10.1007/s10231-008-0075-4. |
[20] |
R. Peng and D. Wei, The periodic-parabolic logistic equation on $\R^N$, Discrete and Continuous Dyn. Syst. Series A, 32 (2012), 619-641. |
[21] |
H. F. Weinberger, Long-time behavior of a class of biological models, SIAM J. Math. Anal., 13 (1982), 353-396.doi: 10.1137/0513028. |
[22] |
X.-Q. Zhao, "Dynamical Systems in Population Biology," Springer-Verlag, New York, 2003. |