Some remarks on traveling wave solutions in competition models

Previous Article
A degenerate diffusion-reaction model of an amensalistic biofilm control system: Existence and simulation of solutions
DCDS-B Home
This Issue
Next Article
Mathematical models of subcutaneous injection of insulin analogues: A mini-review

September 2009, 12(2): 389-399. doi: 10.3934/dcdsb.2009.12.389

Some remarks on traveling wave solutions in competition models

1.	Department of Mathematics, University of Louisville, Louisville, KY 40292

Received December 2008 Revised April 2009 Published July 2009

Abstract
Related Papers

We study the existence of traveling wave solutions for competition models in the form of integro-difference equations. We show that for a two-species competition model it is possible that two species spread at different speeds, and there exists a traveling wave solution. For an $m$-species competition model, under the assumption that species have the same dispersal and growth properties but have different competition abilities, we establish the existence of traveling wave solutions.

Keywords: traveling wave, integro-difference equation., Competition.

Mathematics Subject Classification: Primary: 92D40, 92D25; Secondary: 47G1.

Citation: Bingtuan Li. Some remarks on traveling wave solutions in competition models. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 389-399. doi: 10.3934/dcdsb.2009.12.389

[1]	Haiyan Wang, Carlos Castillo-Chavez. Spreading speeds and traveling waves for non-cooperative integro-difference systems. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 2243-2266. doi: 10.3934/dcdsb.2012.17.2243
[2]	Liang Zhang, Bingtuan Li. Traveling wave solutions in an integro-differential competition model. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 417-428. doi: 10.3934/dcdsb.2012.17.417
[3]	Weiwei Ding, Xing Liang, Bin Xu. Spreading speeds of $N$-season spatially periodic integro-difference models. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3443-3472. doi: 10.3934/dcds.2013.33.3443
[4]	Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations & Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013
[5]	Xiaojie Hou, Yi Li, Kenneth R. Meyer. Traveling wave solutions for a reaction diffusion equation with double degenerate nonlinearities. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 265-290. doi: 10.3934/dcds.2010.26.265
[6]	Bendong Lou. Traveling wave solutions of a generalized curvature flow equation in the plane. Conference Publications, 2007, 2007 (Special) : 687-693. doi: 10.3934/proc.2007.2007.687
[7]	Faustino Sánchez-Garduño, Philip K. Maini, Judith Pérez-Velázquez. A non-linear degenerate equation for direct aggregation and traveling wave dynamics. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 455-487. doi: 10.3934/dcdsb.2010.13.455
[8]	Anna Geyer, Ronald Quirchmayr. Traveling wave solutions of a highly nonlinear shallow water equation. Discrete & Continuous Dynamical Systems - A, 2018, 38 (3) : 1567-1604. doi: 10.3934/dcds.2018065
[9]	Hirokazu Ninomiya. Entire solutions and traveling wave solutions of the Allen-Cahn-Nagumo equation. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 2001-2019. doi: 10.3934/dcds.2019084
[10]	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
[11]	Shujuan Lü, Chunbiao Gan, Baohua Wang, Linning Qian, Meisheng Li. Traveling wave solutions and its stability for 3D Ginzburg-Landau type equation. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 507-527. doi: 10.3934/dcdsb.2011.16.507
[12]	Hisashi Okamoto, Takashi Sakajo, Marcus Wunsch. Steady-states and traveling-wave solutions of the generalized Constantin--Lax--Majda equation. Discrete & Continuous Dynamical Systems - A, 2014, 34 (8) : 3155-3170. doi: 10.3934/dcds.2014.34.3155
[13]	Rui Liu. Some new results on explicit traveling wave solutions of $K(m, n)$ equation. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 633-646. doi: 10.3934/dcdsb.2010.13.633
[14]	Guo Lin, Haiyan Wang. Traveling wave solutions of a reaction-diffusion equation with state-dependent delay. Communications on Pure & Applied Analysis, 2016, 15 (2) : 319-334. doi: 10.3934/cpaa.2016.15.319
[15]	Weiguo Zhang, Yujiao Sun, Zhengming Li, Shengbing Pei, Xiang Li. Bounded traveling wave solutions for MKdV-Burgers equation with the negative dispersive coefficient. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2883-2903. doi: 10.3934/dcdsb.2016078
[16]	Jibin Li, Yi Zhang. On the traveling wave solutions for a nonlinear diffusion-convection equation: Dynamical system approach. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1119-1138. doi: 10.3934/dcdsb.2010.14.1119
[17]	Weiguo Zhang, Yan Zhao, Xiang Li. Qualitative analysis to the traveling wave solutions of Kakutani-Kawahara equation and its approximate damped oscillatory solution. Communications on Pure & Applied Analysis, 2013, 12 (2) : 1075-1090. doi: 10.3934/cpaa.2013.12.1075
[18]	Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control & Related Fields, 2016, 6 (4) : 595-628. doi: 10.3934/mcrf.2016017
[19]	Sebastián Ferrer, Martin Lara. Families of canonical transformations by Hamilton-Jacobi-Poincaré equation. Application to rotational and orbital motion. Journal of Geometric Mechanics, 2010, 2 (3) : 223-241. doi: 10.3934/jgm.2010.2.223
[20]	Manuel de León, Juan Carlos Marrero, David Martín de Diego. Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics. Journal of Geometric Mechanics, 2010, 2 (2) : 159-198. doi: 10.3934/jgm.2010.2.159

2018 Impact Factor: 1.008

American Institute of Mathematical Sciences