-
Previous Article
The logistic map of matrices
- DCDS-B Home
- This Issue
-
Next Article
Phase transitions of a phase field model
Stability of traveling waves for systems of nonlinear integral recursions in spatial population biology
1. | Dept. of Mathematics and Statistics, Georgetown University, Washington DC 20057, United States, United States |
References:
[1] |
O. Diekmann and H. Kaper, On the bounded solutions of a nonlinear convolution equation,, Nonlinear Anal., 2 (1978), 721.
doi: 10.1016/0362-546X(78)90015-9. |
[2] |
R. Fisher, The wave of advance of advantageous genes,, Ann. Eugenics, 7 (1937), 355.
doi: 10.1111/j.1469-1809.1937.tb02153.x. |
[3] |
M. Gil', "Difference Equations in Normed Spaces. Stability and Oscillations,", North-Holland Mathematics Studies 206, (2007). Google Scholar |
[4] |
D. Hardin, P. Takac and G. Webb, A comparison of dispersal strategies for survival of spatially heterogeneous populations,, SIAM J. Appl. Math., 48 (1988), 1396.
doi: 10.1137/0148086. |
[5] |
D. Hardin, P. Takac and G. Webb, Dispersion population models discrete in time and continuous in space,, J. Math. Biol., 28 (1990), 1.
doi: 10.1007/BF00171515. |
[6] |
M. Hassell and H. Comins, Discrete time models for two-species competition,, Theoretical Population Biology, 9 (1976), 202.
doi: 10.1016/0040-5809(76)90045-9. |
[7] |
S. Hsu and X. Zhao, Spreading speeds and traveling waves for nonmonotone integrodifference equations,, SIAM J. Math. Anal., 40 (2008), 776. Google Scholar |
[8] |
A. Kolmogoroff, I. Petrovsky and N. Piscounoff, Éude de l'éuations de la diffusion avec crois-sance de la quantité de matièret son application a un problème biologique,, Bull. Univ. Moscow, 1 (1937), 1. Google Scholar |
[9] |
M. Kot and W. Schaffer, Discrete-time growth-dispersal models,, Math. Biosci., 80 (1986), 109.
doi: 10.1016/0025-5564(86)90069-6. |
[10] |
M. Kot, Discrete-time travelling waves: ecological examples,, J. Math. Biol., 30 (1992), 413.
doi: 10.1007/BF00173295. |
[11] |
M. Kot, M. Lewis and P. van den Driessche, Dispersal data and the spread of invading organisms,, Ecology, 77 (1996), 2027.
doi: 10.2307/2265698. |
[12] |
M. Lewis, B. Li and H. Weinberger, Spreading speed and linear determinacy for two-species competition models,, J. Math. Biol., 45 (2002), 219.
doi: 10.1007/s002850200144. |
[13] |
B. Li, M. Lewis and H. Weinberger, Existence of traveling waves for integral recursions with nonmonotone growth functions,, J. Math. Biol., 58 (2009), 323.
doi: 10.1007/s00285-008-0175-1. |
[14] |
B. Li, H. Weinberger and M. Lewis, Spreading speeds as slowest wave speeds for cooperative systems,, Math. Biosci., 196 (2005), 82.
doi: 10.1016/j.mbs.2005.03.008. |
[15] |
B. Li, Some remarks on traveling wave solutions in competition models,, Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 389.
doi: 10.3934/dcdsb.2009.12.389. |
[16] |
G. Lin and W. Li, Spreading speeds and traveling wavefronts for second order integrodifference equations,, J. Math. Anal. Appl., 361 (2010), 520.
doi: 10.1016/j.jmaa.2009.07.035. |
[17] |
R. Lui, A nonlinear integral operator arising from a model in population genetics. I. Monotone initial data,, SIAM J. Math. Anal., 13 (1982), 913.
doi: 10.1137/0513064. |
[18] |
R. Lui, A nonlinear integral operator arising from a model in population genetics. II. Initial data with compact support,, SIAM J. Math. Anal., 13 (1982), 938.
doi: 10.1137/0513065. |
[19] |
R. Lui, Existence and stability of travelling wave solutions of a nonlinear integral operator,, J. Math. Biol., 16 (): 199. Google Scholar |
[20] |
R. Lui, A nonlinear integral operator arising from a model in population genetics. III. Heterozygote inferior case,, SIAM J. Math. Anal., 16 (1985), 1180.
doi: 10.1137/0516087. |
[21] |
R. Lui, Biological growth and spread modeled by systems of recursions. I. Mathematical theory,, Math. Biosci., 93 (1989), 269.
doi: 10.1016/0025-5564(89)90026-6. |
[22] |
F. Lutscher, Density-dependent dispersal in integrodifference equations,, J. Math. Biol., 56 (2008), 499.
doi: 10.1007/s00285-007-0127-1. |
[23] |
M. Neubert, M. Kot and M. Lewis, Dispersal and pattern-formation in a discrete-time predator-prey model,, Theoretical Population Biology, 48 (1995), 7.
doi: 10.1006/tpbi.1995.1020. |
[24] |
S. Pan and G. Lin, Propagation of second order integrodifference equations with local monotonicity,, Nonlinear Anal. RWA, 12 (2011), 535.
doi: 10.1016/j.nonrwa.2010.06.038. |
[25] |
D. Sattinger, On the stability of waves of nonlinear parabolic systems,, Advances in Math., 22 (1976), 312.
doi: 10.1016/0001-8708(76)90098-0. |
[26] |
J. Travis, D. Murrell and C. Dytham, The evolution of density-dependent dispersal,, Proc. R. Soc. Lond. B, 266 (1999), 1837.
doi: 10.1098/rspb.1999.0854. |
[27] |
R. Veit and M. Lewis, Dispersal, population growth and the Allee Effect: Dynamics of the House Finch invasion of eastern North America,, American Naturalist, 148 (1996), 255.
doi: 10.1086/285924. |
[28] |
D. Volkov and R. Lui, Spreading speed and travelling wave solutions of a partially sedentary population,, IMA J. Appl. Math., 72 (2007), 801.
doi: 10.1093/imamat/hxm025. |
[29] |
H. Wang and C. Castillo-Chavez, Spreading speeds and traveling waves for non-cooperative integro-difference systems,, preprint, (). Google Scholar |
[30] |
H. Weinberger, Asymptotic behavior of a model in population genetics,, in, (1978), 1976. Google Scholar |
[31] |
H. Weinberger, Long-time behavior of a class of biological models,, SIAM J. Math. Anal., 13 (1982), 353.
doi: 10.1137/0513028. |
[32] |
H. Weinberger, M. Lewis and B. Li, Analysis of linear determinacy for spread in cooperative models,, J. Math. Biol., 45 (2002), 183.
doi: 10.1007/s002850200145. |
[33] |
H. Weinberger, M. Lewis and B. Li, Anomalous spreading speeds of cooperative recursion systems,, J. Math. Biol., 55 (2007), 207.
doi: 10.1007/s00285-007-0078-6. |
show all references
References:
[1] |
O. Diekmann and H. Kaper, On the bounded solutions of a nonlinear convolution equation,, Nonlinear Anal., 2 (1978), 721.
doi: 10.1016/0362-546X(78)90015-9. |
[2] |
R. Fisher, The wave of advance of advantageous genes,, Ann. Eugenics, 7 (1937), 355.
doi: 10.1111/j.1469-1809.1937.tb02153.x. |
[3] |
M. Gil', "Difference Equations in Normed Spaces. Stability and Oscillations,", North-Holland Mathematics Studies 206, (2007). Google Scholar |
[4] |
D. Hardin, P. Takac and G. Webb, A comparison of dispersal strategies for survival of spatially heterogeneous populations,, SIAM J. Appl. Math., 48 (1988), 1396.
doi: 10.1137/0148086. |
[5] |
D. Hardin, P. Takac and G. Webb, Dispersion population models discrete in time and continuous in space,, J. Math. Biol., 28 (1990), 1.
doi: 10.1007/BF00171515. |
[6] |
M. Hassell and H. Comins, Discrete time models for two-species competition,, Theoretical Population Biology, 9 (1976), 202.
doi: 10.1016/0040-5809(76)90045-9. |
[7] |
S. Hsu and X. Zhao, Spreading speeds and traveling waves for nonmonotone integrodifference equations,, SIAM J. Math. Anal., 40 (2008), 776. Google Scholar |
[8] |
A. Kolmogoroff, I. Petrovsky and N. Piscounoff, Éude de l'éuations de la diffusion avec crois-sance de la quantité de matièret son application a un problème biologique,, Bull. Univ. Moscow, 1 (1937), 1. Google Scholar |
[9] |
M. Kot and W. Schaffer, Discrete-time growth-dispersal models,, Math. Biosci., 80 (1986), 109.
doi: 10.1016/0025-5564(86)90069-6. |
[10] |
M. Kot, Discrete-time travelling waves: ecological examples,, J. Math. Biol., 30 (1992), 413.
doi: 10.1007/BF00173295. |
[11] |
M. Kot, M. Lewis and P. van den Driessche, Dispersal data and the spread of invading organisms,, Ecology, 77 (1996), 2027.
doi: 10.2307/2265698. |
[12] |
M. Lewis, B. Li and H. Weinberger, Spreading speed and linear determinacy for two-species competition models,, J. Math. Biol., 45 (2002), 219.
doi: 10.1007/s002850200144. |
[13] |
B. Li, M. Lewis and H. Weinberger, Existence of traveling waves for integral recursions with nonmonotone growth functions,, J. Math. Biol., 58 (2009), 323.
doi: 10.1007/s00285-008-0175-1. |
[14] |
B. Li, H. Weinberger and M. Lewis, Spreading speeds as slowest wave speeds for cooperative systems,, Math. Biosci., 196 (2005), 82.
doi: 10.1016/j.mbs.2005.03.008. |
[15] |
B. Li, Some remarks on traveling wave solutions in competition models,, Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 389.
doi: 10.3934/dcdsb.2009.12.389. |
[16] |
G. Lin and W. Li, Spreading speeds and traveling wavefronts for second order integrodifference equations,, J. Math. Anal. Appl., 361 (2010), 520.
doi: 10.1016/j.jmaa.2009.07.035. |
[17] |
R. Lui, A nonlinear integral operator arising from a model in population genetics. I. Monotone initial data,, SIAM J. Math. Anal., 13 (1982), 913.
doi: 10.1137/0513064. |
[18] |
R. Lui, A nonlinear integral operator arising from a model in population genetics. II. Initial data with compact support,, SIAM J. Math. Anal., 13 (1982), 938.
doi: 10.1137/0513065. |
[19] |
R. Lui, Existence and stability of travelling wave solutions of a nonlinear integral operator,, J. Math. Biol., 16 (): 199. Google Scholar |
[20] |
R. Lui, A nonlinear integral operator arising from a model in population genetics. III. Heterozygote inferior case,, SIAM J. Math. Anal., 16 (1985), 1180.
doi: 10.1137/0516087. |
[21] |
R. Lui, Biological growth and spread modeled by systems of recursions. I. Mathematical theory,, Math. Biosci., 93 (1989), 269.
doi: 10.1016/0025-5564(89)90026-6. |
[22] |
F. Lutscher, Density-dependent dispersal in integrodifference equations,, J. Math. Biol., 56 (2008), 499.
doi: 10.1007/s00285-007-0127-1. |
[23] |
M. Neubert, M. Kot and M. Lewis, Dispersal and pattern-formation in a discrete-time predator-prey model,, Theoretical Population Biology, 48 (1995), 7.
doi: 10.1006/tpbi.1995.1020. |
[24] |
S. Pan and G. Lin, Propagation of second order integrodifference equations with local monotonicity,, Nonlinear Anal. RWA, 12 (2011), 535.
doi: 10.1016/j.nonrwa.2010.06.038. |
[25] |
D. Sattinger, On the stability of waves of nonlinear parabolic systems,, Advances in Math., 22 (1976), 312.
doi: 10.1016/0001-8708(76)90098-0. |
[26] |
J. Travis, D. Murrell and C. Dytham, The evolution of density-dependent dispersal,, Proc. R. Soc. Lond. B, 266 (1999), 1837.
doi: 10.1098/rspb.1999.0854. |
[27] |
R. Veit and M. Lewis, Dispersal, population growth and the Allee Effect: Dynamics of the House Finch invasion of eastern North America,, American Naturalist, 148 (1996), 255.
doi: 10.1086/285924. |
[28] |
D. Volkov and R. Lui, Spreading speed and travelling wave solutions of a partially sedentary population,, IMA J. Appl. Math., 72 (2007), 801.
doi: 10.1093/imamat/hxm025. |
[29] |
H. Wang and C. Castillo-Chavez, Spreading speeds and traveling waves for non-cooperative integro-difference systems,, preprint, (). Google Scholar |
[30] |
H. Weinberger, Asymptotic behavior of a model in population genetics,, in, (1978), 1976. Google Scholar |
[31] |
H. Weinberger, Long-time behavior of a class of biological models,, SIAM J. Math. Anal., 13 (1982), 353.
doi: 10.1137/0513028. |
[32] |
H. Weinberger, M. Lewis and B. Li, Analysis of linear determinacy for spread in cooperative models,, J. Math. Biol., 45 (2002), 183.
doi: 10.1007/s002850200145. |
[33] |
H. Weinberger, M. Lewis and B. Li, Anomalous spreading speeds of cooperative recursion systems,, J. Math. Biol., 55 (2007), 207.
doi: 10.1007/s00285-007-0078-6. |
[1] |
Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara, Chang-Hong Wu. The sign of traveling wave speed in bistable dynamics. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3451-3466. doi: 10.3934/dcds.2020047 |
[2] |
Ran Zhang, Shengqiang Liu. On the asymptotic behaviour of traveling wave solution for a discrete diffusive epidemic model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1197-1204. doi: 10.3934/dcdsb.2020159 |
[3] |
Chueh-Hsin Chang, Chiun-Chuan Chen, Chih-Chiang Huang. Traveling wave solutions of a free boundary problem with latent heat effect. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021028 |
[4] |
Yoichi Enatsu, Emiko Ishiwata, Takeo Ushijima. Traveling wave solution for a diffusive simple epidemic model with a free boundary. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 835-850. doi: 10.3934/dcdss.2020387 |
[5] |
Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay. Electronic Research Archive, , () : -. doi: 10.3934/era.2021003 |
[6] |
Mohammad Ghani, Jingyu Li, Kaijun Zhang. Asymptotic stability of traveling fronts to a chemotaxis model with nonlinear diffusion. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021017 |
[7] |
Biyue Chen, Chunxiang Zhao, Chengkui Zhong. The global attractor for the wave equation with nonlocal strong damping. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021015 |
[8] |
Hai-Feng Huo, Shi-Ke Hu, Hong Xiang. Traveling wave solution for a diffusion SEIR epidemic model with self-protection and treatment. Electronic Research Archive, , () : -. doi: 10.3934/era.2020118 |
[9] |
Ching-Hui Wang, Sheng-Chen Fu. Traveling wave solutions to diffusive Holling-Tanner predator-prey models. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021007 |
[10] |
Jonathan J. Wylie, Robert M. Miura, Huaxiong Huang. Systems of coupled diffusion equations with degenerate nonlinear source terms: Linear stability and traveling waves. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 561-569. doi: 10.3934/dcds.2009.23.561 |
[11] |
Xinyu Mei, Yangmin Xiong, Chunyou Sun. Pullback attractor for a weakly damped wave equation with sup-cubic nonlinearity. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 569-600. doi: 10.3934/dcds.2020270 |
[12] |
Takiko Sasaki. Convergence of a blow-up curve for a semilinear wave equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1133-1143. doi: 10.3934/dcdss.2020388 |
[13] |
Reza Chaharpashlou, Abdon Atangana, Reza Saadati. On the fuzzy stability results for fractional stochastic Volterra integral equation. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020432 |
[14] |
Patrick Martinez, Judith Vancostenoble. Lipschitz stability for the growth rate coefficients in a nonlinear Fisher-KPP equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 695-721. doi: 10.3934/dcdss.2020362 |
[15] |
Ahmad Z. Fino, Wenhui Chen. A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5387-5411. doi: 10.3934/cpaa.2020243 |
[16] |
Ludovick Gagnon, José M. Urquiza. Uniform boundary observability with Legendre-Galerkin formulations of the 1-D wave equation. Evolution Equations & Control Theory, 2021, 10 (1) : 129-153. doi: 10.3934/eect.2020054 |
[17] |
Xin-Guang Yang, Lu Li, Xingjie Yan, Ling Ding. The structure and stability of pullback attractors for 3D Brinkman-Forchheimer equation with delay. Electronic Research Archive, 2020, 28 (4) : 1395-1418. doi: 10.3934/era.2020074 |
[18] |
Linglong Du, Min Yang. Pointwise long time behavior for the mixed damped nonlinear wave equation in $ \mathbb{R}^n_+ $. Networks & Heterogeneous Media, 2020 doi: 10.3934/nhm.2020033 |
[19] |
Mokhtari Yacine. Boundary controllability and boundary time-varying feedback stabilization of the 1D wave equation in non-cylindrical domains. Evolution Equations & Control Theory, 2021 doi: 10.3934/eect.2021004 |
[20] |
Christian Aarset, Christian Pötzsche. Bifurcations in periodic integrodifference equations in $ C(\Omega) $ I: Analytical results and applications. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 1-60. doi: 10.3934/dcdsb.2020231 |
2019 Impact Factor: 1.27
Tools
Metrics
Other articles
by authors
[Back to Top]