-
Previous Article
Optimal control of integrodifference equations with growth-harvesting-dispersal order
- DCDS-B Home
- This Issue
-
Next Article
Spreading speeds and traveling waves for non-cooperative integro-difference systems
On sufficient conditions for a linearly determinate spreading speed
1. | School of Mathematics, University of Minnesota, 206 Church Street, Minneapolis, MN 55455, United States |
References:
[1] |
W. C. Allee, "Animal Aggregations. A Study in General Sociology,'' U. of Chicago Press, 1931. |
[2] |
B. H. Gilding and R. Kersner, "Travelling Waves in Nonlinear Diffusion-Convection Reaction," Progress in Nonlinear Differential Equations and their Applications, 60, Birkhäuser Verlag, Basel, 2004. |
[3] |
K. P. Hadeler and F. Rothe, Traveling fronts in nonlinear diffusion equations, J. Math. Biol., 2 (1975), 251-263. |
[4] |
A. N. Kolmogorov, I. G. Petrovski and N. S. Piscounov, Étude de l'équation de la diffusion avec croissance de la quantité de matiére et son application á un probléme biologique, Bull. Univ. d'État á Moscou Ser. Intern., 1 (1937), 1-26. |
[5] |
M.-H. Wang and M. Kot, Speeds of invasion in a model with strong or weak Allee effects, Mathematical Biosciences, 171 (2001), 83-97.
doi: 10.1016/S0025-5564(01)00048-7. |
show all references
References:
[1] |
W. C. Allee, "Animal Aggregations. A Study in General Sociology,'' U. of Chicago Press, 1931. |
[2] |
B. H. Gilding and R. Kersner, "Travelling Waves in Nonlinear Diffusion-Convection Reaction," Progress in Nonlinear Differential Equations and their Applications, 60, Birkhäuser Verlag, Basel, 2004. |
[3] |
K. P. Hadeler and F. Rothe, Traveling fronts in nonlinear diffusion equations, J. Math. Biol., 2 (1975), 251-263. |
[4] |
A. N. Kolmogorov, I. G. Petrovski and N. S. Piscounov, Étude de l'équation de la diffusion avec croissance de la quantité de matiére et son application á un probléme biologique, Bull. Univ. d'État á Moscou Ser. Intern., 1 (1937), 1-26. |
[5] |
M.-H. Wang and M. Kot, Speeds of invasion in a model with strong or weak Allee effects, Mathematical Biosciences, 171 (2001), 83-97.
doi: 10.1016/S0025-5564(01)00048-7. |
[1] |
Manjun Ma, Xiao-Qiang Zhao. Monostable waves and spreading speed for a reaction-diffusion model with seasonal succession. Discrete and Continuous Dynamical Systems - B, 2016, 21 (2) : 591-606. doi: 10.3934/dcdsb.2016.21.591 |
[2] |
Zhenguo Bai, Tingting Zhao. Spreading speed and traveling waves for a non-local delayed reaction-diffusion system without quasi-monotonicity. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4063-4085. doi: 10.3934/dcdsb.2018126 |
[3] |
Juliette Bouhours, Grégroie Nadin. A variational approach to reaction-diffusion equations with forced speed in dimension 1. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 1843-1872. doi: 10.3934/dcds.2015.35.1843 |
[4] |
Hideki Murakawa. Fast reaction limit of reaction-diffusion systems. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 1047-1062. doi: 10.3934/dcdss.2020405 |
[5] |
Gregoire Nadin. How does the spreading speed associated with the Fisher-KPP equation depend on random stationary diffusion and reaction terms?. Discrete and Continuous Dynamical Systems - B, 2015, 20 (6) : 1785-1803. doi: 10.3934/dcdsb.2015.20.1785 |
[6] |
Ching-Shan Chou, Yong-Tao Zhang, Rui Zhao, Qing Nie. Numerical methods for stiff reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2007, 7 (3) : 515-525. doi: 10.3934/dcdsb.2007.7.515 |
[7] |
Laurent Desvillettes, Klemens Fellner. Entropy methods for reaction-diffusion systems. Conference Publications, 2007, 2007 (Special) : 304-312. doi: 10.3934/proc.2007.2007.304 |
[8] |
A. Dall'Acqua. Positive solutions for a class of reaction-diffusion systems. Communications on Pure and Applied Analysis, 2003, 2 (1) : 65-76. doi: 10.3934/cpaa.2003.2.65 |
[9] |
Bingtuan Li, William F. Fagan, Garrett Otto, Chunwei Wang. Spreading speeds and traveling wave solutions in a competitive reaction-diffusion model for species persistence in a stream. Discrete and Continuous Dynamical Systems - B, 2014, 19 (10) : 3267-3281. doi: 10.3934/dcdsb.2014.19.3267 |
[10] |
Hans F. Weinberger, Kohkichi Kawasaki, Nanako Shigesada. Spreading speeds for a partially cooperative 2-species reaction-diffusion model. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 1087-1098. doi: 10.3934/dcds.2009.23.1087 |
[11] |
Grégory Faye, Thomas Giletti, Matt Holzer. Asymptotic spreading for Fisher-KPP reaction-diffusion equations with heterogeneous shifting diffusivity. Discrete and Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021146 |
[12] |
Henri Berestycki, Luca Rossi. Reaction-diffusion equations for population dynamics with forced speed I - The case of the whole space. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 41-67. doi: 10.3934/dcds.2008.21.41 |
[13] |
Henri Berestycki, Luca Rossi. Reaction-diffusion equations for population dynamics with forced speed II - cylindrical-type domains. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 19-61. doi: 10.3934/dcds.2009.25.19 |
[14] |
Yong Jung Kim, Wei-Ming Ni, Masaharu Taniguchi. Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3707-3718. doi: 10.3934/dcds.2013.33.3707 |
[15] |
Dieter Bothe, Michel Pierre. The instantaneous limit for reaction-diffusion systems with a fast irreversible reaction. Discrete and Continuous Dynamical Systems - S, 2012, 5 (1) : 49-59. doi: 10.3934/dcdss.2012.5.49 |
[16] |
Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189 |
[17] |
Masaharu Taniguchi. Instability of planar traveling waves in bistable reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2003, 3 (1) : 21-44. doi: 10.3934/dcdsb.2003.3.21 |
[18] |
Wei Feng, Weihua Ruan, Xin Lu. On existence of wavefront solutions in mixed monotone reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2016, 21 (3) : 815-836. doi: 10.3934/dcdsb.2016.21.815 |
[19] |
C. van der Mee, Stella Vernier Piro. Travelling waves for solid-gas reaction-diffusion systems. Conference Publications, 2003, 2003 (Special) : 872-879. doi: 10.3934/proc.2003.2003.872 |
[20] |
Shin-Ichiro Ei, Toshio Ishimoto. Effect of boundary conditions on the dynamics of a pulse solution for reaction-diffusion systems. Networks and Heterogeneous Media, 2013, 8 (1) : 191-209. doi: 10.3934/nhm.2013.8.191 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]