[1]
|
A. Bourgeois, Spreading speeds and travelling waves in integrodifference equations with overcompensatory dynamics, Master Thesis, University of Ottawa, 2016.
Google Scholar
|
[2]
|
A. Bourgeois, V. LeBlanc and F. Lutscher, Spreading phenomena in integrodifference equations with nonmonotone growth functions, SIAM J. Appl. Math., 2018, 78, 2950-2972. doi: 10.1137/17M1126102
CrossRef Google Scholar
|
[3]
|
J. Fang and X. Zhao, Traveling waves for monotone semiflows with weak compactness, SIAM J. Math. Anal., 2014, 46, 3678-3704. doi: 10.1137/140953939
CrossRef Google Scholar
|
[4]
|
S. B. Hsu and X. Zhao, Spreading speeds and traveling waves for nonmonotone integrodifference equations, SIAM J. Math. Anal., 2008, 40, 776-789. doi: 10.1137/070703016
CrossRef Google Scholar
|
[5]
|
J. Huang and X. Zou, Existence of travelling wavefronts of delayed reaction-diffusion systems without monotonicity, Discrete Conti. Dyn. Sys., 2003, 9, 925-936. doi: 10.3934/dcds.2003.9.925
CrossRef Google Scholar
|
[6]
|
M. Kot, Discrete-time travelling waves: Ecological examples, J. Math. Biol., 1992, 30, 413-436.
Google Scholar
|
[7]
|
M. Kot and W. M. Schaffer, Discrete-time growth-dispersal models, Math. Biosci., 1986, 80, 109-136. doi: 10.1016/0025-5564(86)90069-6
CrossRef Google Scholar
|
[8]
|
B. Li, M. A. Lewis and H. F. Weinberger, Existence of traveling waves for integral recursions with nonmonotone growth functions, J. Math. Biol., 2009, 58, 323-338. doi: 10.1007/s00285-008-0175-1
CrossRef Google Scholar
|
[9]
|
X. Liang and X. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 2007, 60, 1-40. doi: 10.1002/cpa.20154
CrossRef Google Scholar
|
[10]
|
G. Lin, Travelling wave solutions for intefro-difference systems, J. Differential Equations, 2015, 258, 2908-2940. doi: 10.1016/j.jde.2014.12.030
CrossRef Google Scholar
|
[11]
|
G. Lin, W. Li and S. Ruan, Asymptotic stability of monostable wavefronts in discrete-time integral recursions, Sci. China Math., 2010, 53, 1185-1194. doi: 10.1007/s11425-009-0123-6
CrossRef Google Scholar
|
[12]
|
R. Lui, Biological growth and spread modeled by systems of recursions. I Mathematical theory, Math. Biosci., 1989, 93, 269-295. doi: 10.1016/0025-5564(89)90026-6
CrossRef Google Scholar
|
[13]
|
F. Lutscher, Integrodifference Equations in Spatial Ecology, Springer, Cham, 2019.
Google Scholar
|
[14]
|
S. Ma, Traveling wavefronts for delayed reaction-diffusion systems via a fixed point theorem, J. Differential Equations, 2001, 171, 294-314. doi: 10.1006/jdeq.2000.3846
CrossRef Google Scholar
|
[15]
|
R. M. May, Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos, Science, 1974, 186, 645-647. doi: 10.1126/science.186.4164.645
CrossRef Google Scholar
|
[16]
|
D. Mollison, Spatial contact models for ecological and epidemic spread, J. Roy. Statist. Soc. Ser. B, 1977, 39, 283-326.
Google Scholar
|
[17]
|
M. Neubert, M. Kot and M. A. Lewis, Dispersal and pattern formation in a discrete-time predator-prey model, Theoret. Popul. Biol., 1995, 48, 7-43. doi: 10.1006/tpbi.1995.1020
CrossRef Google Scholar
|
[18]
|
Y. Pan, New methods for the existence and uniqueness of traveling waves of non-monotone integro-difference equations with applications, J. Differential Equations, 2020, 268, 6319-6349. doi: 10.1016/j.jde.2019.11.030
CrossRef Google Scholar
|
[19]
|
Y. Pan, J. Fang and J. Wei, Seasonal influence on age-structured invasive species with yearly generation, SIAM J. Appl. Math., 2018, 78, 1842-1862. doi: 10.1137/17M1145690
CrossRef Google Scholar
|
[20]
|
M. Slatkin, Gene flow and selection in a cline, Genetics, 1973, 75, 733-756. doi: 10.1093/genetics/75.4.733
CrossRef Google Scholar
|
[21]
|
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, AMS, Providence, RI, 1995.
Google Scholar
|
[22]
|
H. F. Weinberger, Long-time behavior of a class of biological model, SIAM J. Math. Anal., 1982, 13, 353-396. doi: 10.1137/0513028
CrossRef Google Scholar
|
[23]
|
H. F. Weinberger, M. A. Lewis and B. Li, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol., 2002, 45, 183-218. doi: 10.1007/s002850200145
CrossRef Google Scholar
|
[24]
|
J. Wu and X. Zou, Traveling wave fronts of reaction-diffusion systems with delay, J. Dynam. Diff. Eqns., 2001, 13, 651-687. doi: 10.1023/A:1016690424892
CrossRef Google Scholar
|
[25]
|
T. Yi, Y. Chen and J. Wu, Unimodal dynamical systems: Comparison principles, spreading speeds and travelling waves, J. Differential Equations, 2013, 254, 3538-3572. doi: 10.1016/j.jde.2013.01.031
CrossRef Google Scholar
|
[26]
|
Z. Yu and R. Yuan, Properties of traveling waves for integrodifference equations with nonmonotone growth functions, Z. Angew. Math. Phys., 2012, 63, 249-259. doi: 10.1007/s00033-011-0170-z
CrossRef Google Scholar
|
[27]
|
L. Zhang and S. Pan, Entire solutions of integrodifference equations, J. Difference Equ. Appl., 2019, 25, 504-515. doi: 10.1080/10236198.2019.1583748
CrossRef Google Scholar
|