-
Previous Article
Attractors for autonomous and nonautonomous 3D Navier-Stokes-Voight equations
- DCDS-B Home
- This Issue
-
Next Article
The flashing ratchet and unidirectional transport of matter
Existence of traveling wavefront for discrete bistable competition model
1. | Department of Applied Mathematics, National Chung Hsing University, 250, Kuo Kuang Road, Taichung 402, Taiwan |
References:
[1] |
X. Chen, J. S. Guo and C. C. Wu, Traveling waves in discrete periodic media for bistable dynamics, Arch. Rational Mech. Anal., 189 (2008), 189-236.
doi: 10.1007/s00205-007-0103-3. |
[2] |
C. Conley and R. Gardner, An application of the generalized Morse index to traveling wave solutions of a competitive reaction diffusion model, Indiana Univ. Math. J., 33 (1984), 319-343.
doi: 10.1512/iumj.1984.33.33018. |
[3] |
R. A. Gardner, Existence and stability of traveling wave solutions of competition models: a degree theoretic, J. Differential Equations, 44 (1982), 343-364.
doi: 10.1016/0022-0396(82)90001-8. |
[4] |
J. S. Guo and C. H. Wu, Traveling wave front for a two-component lattice dynamical system arising in competition models, preprint. |
[5] |
J. S. Guo and C. H. Wu, Wave propagation for a two-component lattice dynamical system arising in strong competition models, J. Differential Equations, 250 (2011), 3504-3533.
doi: 10.1016/j.jde.2010.12.004. |
[6] |
Y. Hosono, Singular perturbation analysis of travelling waves for diffusive Lotka-Volterra competitive models, Numerical and Applied Mathematics, Part II (Paris, 1988), Baltzer, Basel, (1989), 687-692. |
[7] |
Y. Hosono, The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model, Bulletin of Math. Biology, 60 (1998), 435-448.
doi: 10.1006/bulm.1997.0008. |
[8] |
Y. Kan-on, Fisher wave fronts for the Lotka-Volterra competition model with diffusion, Nonlinear Anal., 28 (1997), 145-164. |
[9] |
J. P. Keener, Propagation and its failure in coupled systems of discrete excitable cells, SIAM J. Appl. Math., 47 (1987), 556-572.
doi: 10.1137/0147038. |
[10] |
A. Okubo, P. K. Maini, M. H. Williamson and J. D. Murray, On the spatial spread of the grey squirrel in Britain, Proc. R. Soc. Lond. B, 238 (1989), 113-125.
doi: 10.1098/rspb.1989.0070. |
[11] |
M. M. Tang and P. C. Fife, Propagating fronts for competing species equations with diffusion, Arch. Rational Mech. Anal., 73 (1980), 69-77.
doi: 10.1007/BF00283257. |
show all references
References:
[1] |
X. Chen, J. S. Guo and C. C. Wu, Traveling waves in discrete periodic media for bistable dynamics, Arch. Rational Mech. Anal., 189 (2008), 189-236.
doi: 10.1007/s00205-007-0103-3. |
[2] |
C. Conley and R. Gardner, An application of the generalized Morse index to traveling wave solutions of a competitive reaction diffusion model, Indiana Univ. Math. J., 33 (1984), 319-343.
doi: 10.1512/iumj.1984.33.33018. |
[3] |
R. A. Gardner, Existence and stability of traveling wave solutions of competition models: a degree theoretic, J. Differential Equations, 44 (1982), 343-364.
doi: 10.1016/0022-0396(82)90001-8. |
[4] |
J. S. Guo and C. H. Wu, Traveling wave front for a two-component lattice dynamical system arising in competition models, preprint. |
[5] |
J. S. Guo and C. H. Wu, Wave propagation for a two-component lattice dynamical system arising in strong competition models, J. Differential Equations, 250 (2011), 3504-3533.
doi: 10.1016/j.jde.2010.12.004. |
[6] |
Y. Hosono, Singular perturbation analysis of travelling waves for diffusive Lotka-Volterra competitive models, Numerical and Applied Mathematics, Part II (Paris, 1988), Baltzer, Basel, (1989), 687-692. |
[7] |
Y. Hosono, The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model, Bulletin of Math. Biology, 60 (1998), 435-448.
doi: 10.1006/bulm.1997.0008. |
[8] |
Y. Kan-on, Fisher wave fronts for the Lotka-Volterra competition model with diffusion, Nonlinear Anal., 28 (1997), 145-164. |
[9] |
J. P. Keener, Propagation and its failure in coupled systems of discrete excitable cells, SIAM J. Appl. Math., 47 (1987), 556-572.
doi: 10.1137/0147038. |
[10] |
A. Okubo, P. K. Maini, M. H. Williamson and J. D. Murray, On the spatial spread of the grey squirrel in Britain, Proc. R. Soc. Lond. B, 238 (1989), 113-125.
doi: 10.1098/rspb.1989.0070. |
[11] |
M. M. Tang and P. C. Fife, Propagating fronts for competing species equations with diffusion, Arch. Rational Mech. Anal., 73 (1980), 69-77.
doi: 10.1007/BF00283257. |
[1] |
Jong-Shenq Guo, Ying-Chih Lin. Traveling wave solution for a lattice dynamical system with convolution type nonlinearity. Discrete and Continuous Dynamical Systems, 2012, 32 (1) : 101-124. doi: 10.3934/dcds.2012.32.101 |
[2] |
Shi-Liang Wu, Cheng-Hsiung Hsu. Entire solutions with merging fronts to a bistable periodic lattice dynamical system. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 2329-2346. doi: 10.3934/dcds.2016.36.2329 |
[3] |
Cui-Ping Cheng, Ruo-Fan An. Global stability of traveling wave fronts in a two-dimensional lattice dynamical system with global interaction. Electronic Research Archive, 2021, 29 (5) : 3535-3550. doi: 10.3934/era.2021051 |
[4] |
Chin-Chin Wu. Monotonicity and uniqueness of wave profiles for a three components lattice dynamical system. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2813-2827. doi: 10.3934/dcds.2017121 |
[5] |
Liang Zhang, Bingtuan Li. Traveling wave solutions in an integro-differential competition model. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 417-428. doi: 10.3934/dcdsb.2012.17.417 |
[6] |
Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara, Chang-Hong Wu. The sign of traveling wave speed in bistable dynamics. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3451-3466. doi: 10.3934/dcds.2020047 |
[7] |
Chiun-Chuan Chen, Ting-Yang Hsiao, Li-Chang Hung. Discrete N-barrier maximum principle for a lattice dynamical system arising in competition models. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 153-187. doi: 10.3934/dcds.2020007 |
[8] |
Zhaoquan Xu, Jiying Ma. Monotonicity, asymptotics and uniqueness of travelling wave solution of a non-local delayed lattice dynamical system. Discrete and Continuous Dynamical Systems, 2015, 35 (10) : 5107-5131. doi: 10.3934/dcds.2015.35.5107 |
[9] |
Bingtuan Li. Some remarks on traveling wave solutions in competition models. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 389-399. doi: 10.3934/dcdsb.2009.12.389 |
[10] |
Fengxin Chen. Stability and uniqueness of traveling waves for system of nonlocal evolution equations with bistable nonlinearity. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 659-673. doi: 10.3934/dcds.2009.24.659 |
[11] |
Jibin Li, Yi Zhang. On the traveling wave solutions for a nonlinear diffusion-convection equation: Dynamical system approach. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 1119-1138. doi: 10.3934/dcdsb.2010.14.1119 |
[12] |
E. S. Van Vleck, Aijun Zhang. Competing interactions and traveling wave solutions in lattice differential equations. Communications on Pure and Applied Analysis, 2016, 15 (2) : 457-475. doi: 10.3934/cpaa.2016.15.457 |
[13] |
Cheng-Hsiung Hsu, Jian-Jhong Lin. Stability analysis of traveling wave solutions for lattice reaction-diffusion equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1757-1774. doi: 10.3934/dcdsb.2020001 |
[14] |
Guo-Bao Zhang, Ruyun Ma, Xue-Shi Li. Traveling waves of a Lotka-Volterra strong competition system with nonlocal dispersal. Discrete and Continuous Dynamical Systems - B, 2018, 23 (2) : 587-608. doi: 10.3934/dcdsb.2018035 |
[15] |
Xiaojie Hou, Yi Li. Traveling waves in a three species competition-cooperation system. Communications on Pure and Applied Analysis, 2017, 16 (4) : 1103-1120. doi: 10.3934/cpaa.2017053 |
[16] |
Caibin Zeng, Xiaofang Lin, Jianhua Huang, Qigui Yang. Pathwise solution to rough stochastic lattice dynamical system driven by fractional noise. Communications on Pure and Applied Analysis, 2020, 19 (2) : 811-834. doi: 10.3934/cpaa.2020038 |
[17] |
Fang-Di Dong, Wan-Tong Li, Li Zhang. Entire solutions in a two-dimensional nonlocal lattice dynamical system. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2517-2545. doi: 10.3934/cpaa.2018120 |
[18] |
Ahmed Y. Abdallah. Upper semicontinuity of the attractor for a second order lattice dynamical system. Discrete and Continuous Dynamical Systems - B, 2005, 5 (4) : 899-916. doi: 10.3934/dcdsb.2005.5.899 |
[19] |
Jong-Shenq Guo, Chang-Hong Wu. Front propagation for a two-dimensional periodic monostable lattice dynamical system. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 197-223. doi: 10.3934/dcds.2010.26.197 |
[20] |
Wenzhang Huang. Weakly coupled traveling waves for a model of growth and competition in a flow reactor. Mathematical Biosciences & Engineering, 2006, 3 (1) : 79-87. doi: 10.3934/mbe.2006.3.79 |
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]