October  2011, 16(3): 973-984. doi: 10.3934/dcdsb.2011.16.973

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

Received  September 2010 Revised  January 2011 Published  June 2011

We study traveling wavefront solutions for a two-component competition system on a one-dimensional lattice. We combine the monotonic iteration method with a truncation to obtain the existence of the traveling wavefront solution.
Citation: Chin-Chin Wu. Existence of traveling wavefront for discrete bistable competition model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 973-984. doi: 10.3934/dcdsb.2011.16.973
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. doi: 10.1007/s00205-007-0103-3. Google Scholar

[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. doi: 10.1512/iumj.1984.33.33018. Google Scholar

[3]

R. A. Gardner, Existence and stability of traveling wave solutions of competition models: a degree theoretic,, J. Differential Equations, 44 (1982), 343. doi: 10.1016/0022-0396(82)90001-8. Google Scholar

[4]

J. S. Guo and C. H. Wu, Traveling wave front for a two-component lattice dynamical system arising in competition models,, preprint., (). Google Scholar

[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. doi: 10.1016/j.jde.2010.12.004. Google Scholar

[6]

Y. Hosono, Singular perturbation analysis of travelling waves for diffusive Lotka-Volterra competitive models,, Numerical and Applied Mathematics, (1989), 687. Google Scholar

[7]

Y. Hosono, The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model,, Bulletin of Math. Biology, 60 (1998), 435. doi: 10.1006/bulm.1997.0008. Google Scholar

[8]

Y. Kan-on, Fisher wave fronts for the Lotka-Volterra competition model with diffusion,, Nonlinear Anal., 28 (1997), 145. Google Scholar

[9]

J. P. Keener, Propagation and its failure in coupled systems of discrete excitable cells,, SIAM J. Appl. Math., 47 (1987), 556. doi: 10.1137/0147038. Google Scholar

[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. doi: 10.1098/rspb.1989.0070. Google Scholar

[11]

M. M. Tang and P. C. Fife, Propagating fronts for competing species equations with diffusion,, Arch. Rational Mech. Anal., 73 (1980), 69. doi: 10.1007/BF00283257. Google Scholar

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. doi: 10.1007/s00205-007-0103-3. Google Scholar

[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. doi: 10.1512/iumj.1984.33.33018. Google Scholar

[3]

R. A. Gardner, Existence and stability of traveling wave solutions of competition models: a degree theoretic,, J. Differential Equations, 44 (1982), 343. doi: 10.1016/0022-0396(82)90001-8. Google Scholar

[4]

J. S. Guo and C. H. Wu, Traveling wave front for a two-component lattice dynamical system arising in competition models,, preprint., (). Google Scholar

[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. doi: 10.1016/j.jde.2010.12.004. Google Scholar

[6]

Y. Hosono, Singular perturbation analysis of travelling waves for diffusive Lotka-Volterra competitive models,, Numerical and Applied Mathematics, (1989), 687. Google Scholar

[7]

Y. Hosono, The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model,, Bulletin of Math. Biology, 60 (1998), 435. doi: 10.1006/bulm.1997.0008. Google Scholar

[8]

Y. Kan-on, Fisher wave fronts for the Lotka-Volterra competition model with diffusion,, Nonlinear Anal., 28 (1997), 145. Google Scholar

[9]

J. P. Keener, Propagation and its failure in coupled systems of discrete excitable cells,, SIAM J. Appl. Math., 47 (1987), 556. doi: 10.1137/0147038. Google Scholar

[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. doi: 10.1098/rspb.1989.0070. Google Scholar

[11]

M. M. Tang and P. C. Fife, Propagating fronts for competing species equations with diffusion,, Arch. Rational Mech. Anal., 73 (1980), 69. doi: 10.1007/BF00283257. Google Scholar

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