
-
Previous Article
Singularities of certain finite energy solutions to the Navier-Stokes system
- DCDS Home
- This Issue
-
Next Article
Non-potential and non-radial Dirichlet systems with mean curvature operator in Minkowski space
Discrete N-barrier maximum principle for a lattice dynamical system arising in competition models
1. | Department of Mathematics, National Taiwan University, National Center for Theoretical Sciences, Taipei, Taiwan |
2. | Department of Mathematics, National Taiwan University, Taipei, Taiwan |
In the present paper, we show that an analogous N-barrier maximum principle (see [
References:
[1] |
R. A. Armstrong and R. McGehee,
Competitive exclusion, Amer. Natur., 115 (1980), 151-170.
doi: 10.1086/283553. |
[2] |
Cantrell, Ward and Jr.,
On competition-mediated coexistence, SIAM J. Appl. Math., 57 (1997), 1311-1327.
doi: 10.1137/S0036139995292367. |
[3] |
C.-C. Chen and L.-C. Hung,
A maximum principle for diffusive lotka-volterra systems of two competing species, J. Differential Equations, 261 (2016), 4573-4592.
doi: 10.1016/j.jde.2016.07.001. |
[4] |
C.-C. Chen and L.-C. Hung,
Nonexistence of traveling wave solutions, exact and semi-exact traveling wave solutions for diffusive Lotka-Volterra systems of three competing species, Commun. Pure Appl. Anal., 15 (2016), 1451-1469.
doi: 10.3934/cpaa.2016.15.1451. |
[5] |
C.-C. Chen and L.-C. Hung,
An N-barrier maximum principle for elliptic systems arising from the study of traveling waves in reaction-diffusion systems, Discrete Contin. Dyn. Syst. B, 23 (2018), 1503-1521.
doi: 10.3934/dcdsb.2018054. |
[6] |
C.-C. Chen, L.-C. Hung and C.-C. Lai,
An N-barrier maximum principle for autonomous systems of n species and its application to problems arising from population dynamics, Commun. Pure Appl. Anal., 18 (2019), 33-50.
doi: 10.3934/cpaa.2019003. |
[7] |
C.-C. Chen, L.-C. Hung and H.-F. Liu,
N-barrier maximum principle for degenerate elliptic systems and its application, Discrete Contin. Dyn. Syst. A, 38 (2018), 791-821.
doi: 10.3934/dcds.2018034. |
[8] |
C.-C. Chen, L.-C. Hung, M. Mimura, M. Tohma and D. Ueyama,
Semi-exact equilibrium solutions for three-species competition-diffusion systems, Hiroshima Math J., 43 (2013), 179-206.
doi: 10.32917/hmj/1372180511. |
[9] |
C.-C. Chen, L.-C. Hung, M. Mimura and D. Ueyama,
Exact travelling wave solutions of three-species competition-diffusion systems, Discrete Contin. Dyn. Syst. Ser. B, 17 (2012), 2653-2669.
doi: 10.3934/dcdsb.2012.17.2653. |
[10] |
P. de Mottoni, Qualitative analysis for some quasilinear parabolic systems, Institute of Math., Polish Academy Sci., 11 (1979), p190. |
[11] |
J.-S. Guo and C.-C. Wu,
The existence of traveling wave solutions for a bistable three-component lattice dynamical system, J. Differential Equations, 260 (2016), 1445-1455.
doi: 10.1016/j.jde.2015.09.036. |
[12] |
J.-S. Guo and C.-H. Wu,
Wave propagation for a two-component lattice dynamical system arising in strong competition models, Journal of Differential Equations, 250 (2011), 3504-3533.
doi: 10.1016/j.jde.2010.12.004. |
[13] |
J.-S. Guo and C.-H. Wu,
Traveling wave front for a two-component lattice dynamical system arising in competition models, Journal of Differential Equations, 252 (2012), 4357-4391.
doi: 10.1016/j.jde.2012.01.009. |
[14] |
S.-B. Hsu and T.-H. Hsu,
Competitive exclusion of microbial species for a single nutrient with internal storage, SIAM J. Appl. Math., 68 (2008), 1600-1617.
doi: 10.1137/070700784. |
[15] |
S. B. Hsu, H. L. Smith and P. Waltman,
Competitive exclusion and coexistence for competitive systems on ordered Banach spaces, Trans. Amer. Math. Soc., 348 (1996), 4083-4094.
doi: 10.1090/S0002-9947-96-01724-2. |
[16] |
L.-C. Hung,
Exact traveling wave solutions for diffusive Lotka-Volterra systems of two competing species, Jpn. J. Ind. Appl. Math., 29 (2012), 237-251.
doi: 10.1007/s13160-012-0056-2. |
[17] |
S. R.-J. Jang,
Competitive exclusion and coexistence in a Leslie-Gower competition model with Allee effects, Appl. Anal., 92 (2013), 1527-1540.
doi: 10.1080/00036811.2012.692365. |
[18] |
Y. Kan-on,
Parameter dependence of propagation speed of travelling waves for competition-diffusion equations, SIAM J. Math. Anal., 26 (1995), 340-363.
doi: 10.1137/S0036141093244556. |
[19] |
J. Kastendiek,
Competitor-mediated coexistence: Interactions among three species of benthic macroalgae, Journal of Experimental Marine Biology and Ecology, 62 (1982), 201-210.
|
[20] |
R. McGehee and R. A. Armstrong,
Some mathematical problems concerning the ecological principle of competitive exclusion, J. Differential Equations, 23 (1977), 30-52.
doi: 10.1016/0022-0396(77)90135-8. |
[21] |
M. Mimura and M. Tohma,
Dynamic coexistence in a three-species competition–diffusion system, Ecological Complexity, 21 (2015), 215-232.
|
[22] |
H. L. Smith and P. Waltman,
Competition for a single limiting resource in continuous culture: the variable-yield model, SIAM J. Appl. Math., 54 (1994), 1113-1131.
doi: 10.1137/S0036139993245344. |
show all references
References:
[1] |
R. A. Armstrong and R. McGehee,
Competitive exclusion, Amer. Natur., 115 (1980), 151-170.
doi: 10.1086/283553. |
[2] |
Cantrell, Ward and Jr.,
On competition-mediated coexistence, SIAM J. Appl. Math., 57 (1997), 1311-1327.
doi: 10.1137/S0036139995292367. |
[3] |
C.-C. Chen and L.-C. Hung,
A maximum principle for diffusive lotka-volterra systems of two competing species, J. Differential Equations, 261 (2016), 4573-4592.
doi: 10.1016/j.jde.2016.07.001. |
[4] |
C.-C. Chen and L.-C. Hung,
Nonexistence of traveling wave solutions, exact and semi-exact traveling wave solutions for diffusive Lotka-Volterra systems of three competing species, Commun. Pure Appl. Anal., 15 (2016), 1451-1469.
doi: 10.3934/cpaa.2016.15.1451. |
[5] |
C.-C. Chen and L.-C. Hung,
An N-barrier maximum principle for elliptic systems arising from the study of traveling waves in reaction-diffusion systems, Discrete Contin. Dyn. Syst. B, 23 (2018), 1503-1521.
doi: 10.3934/dcdsb.2018054. |
[6] |
C.-C. Chen, L.-C. Hung and C.-C. Lai,
An N-barrier maximum principle for autonomous systems of n species and its application to problems arising from population dynamics, Commun. Pure Appl. Anal., 18 (2019), 33-50.
doi: 10.3934/cpaa.2019003. |
[7] |
C.-C. Chen, L.-C. Hung and H.-F. Liu,
N-barrier maximum principle for degenerate elliptic systems and its application, Discrete Contin. Dyn. Syst. A, 38 (2018), 791-821.
doi: 10.3934/dcds.2018034. |
[8] |
C.-C. Chen, L.-C. Hung, M. Mimura, M. Tohma and D. Ueyama,
Semi-exact equilibrium solutions for three-species competition-diffusion systems, Hiroshima Math J., 43 (2013), 179-206.
doi: 10.32917/hmj/1372180511. |
[9] |
C.-C. Chen, L.-C. Hung, M. Mimura and D. Ueyama,
Exact travelling wave solutions of three-species competition-diffusion systems, Discrete Contin. Dyn. Syst. Ser. B, 17 (2012), 2653-2669.
doi: 10.3934/dcdsb.2012.17.2653. |
[10] |
P. de Mottoni, Qualitative analysis for some quasilinear parabolic systems, Institute of Math., Polish Academy Sci., 11 (1979), p190. |
[11] |
J.-S. Guo and C.-C. Wu,
The existence of traveling wave solutions for a bistable three-component lattice dynamical system, J. Differential Equations, 260 (2016), 1445-1455.
doi: 10.1016/j.jde.2015.09.036. |
[12] |
J.-S. Guo and C.-H. Wu,
Wave propagation for a two-component lattice dynamical system arising in strong competition models, Journal of Differential Equations, 250 (2011), 3504-3533.
doi: 10.1016/j.jde.2010.12.004. |
[13] |
J.-S. Guo and C.-H. Wu,
Traveling wave front for a two-component lattice dynamical system arising in competition models, Journal of Differential Equations, 252 (2012), 4357-4391.
doi: 10.1016/j.jde.2012.01.009. |
[14] |
S.-B. Hsu and T.-H. Hsu,
Competitive exclusion of microbial species for a single nutrient with internal storage, SIAM J. Appl. Math., 68 (2008), 1600-1617.
doi: 10.1137/070700784. |
[15] |
S. B. Hsu, H. L. Smith and P. Waltman,
Competitive exclusion and coexistence for competitive systems on ordered Banach spaces, Trans. Amer. Math. Soc., 348 (1996), 4083-4094.
doi: 10.1090/S0002-9947-96-01724-2. |
[16] |
L.-C. Hung,
Exact traveling wave solutions for diffusive Lotka-Volterra systems of two competing species, Jpn. J. Ind. Appl. Math., 29 (2012), 237-251.
doi: 10.1007/s13160-012-0056-2. |
[17] |
S. R.-J. Jang,
Competitive exclusion and coexistence in a Leslie-Gower competition model with Allee effects, Appl. Anal., 92 (2013), 1527-1540.
doi: 10.1080/00036811.2012.692365. |
[18] |
Y. Kan-on,
Parameter dependence of propagation speed of travelling waves for competition-diffusion equations, SIAM J. Math. Anal., 26 (1995), 340-363.
doi: 10.1137/S0036141093244556. |
[19] |
J. Kastendiek,
Competitor-mediated coexistence: Interactions among three species of benthic macroalgae, Journal of Experimental Marine Biology and Ecology, 62 (1982), 201-210.
|
[20] |
R. McGehee and R. A. Armstrong,
Some mathematical problems concerning the ecological principle of competitive exclusion, J. Differential Equations, 23 (1977), 30-52.
doi: 10.1016/0022-0396(77)90135-8. |
[21] |
M. Mimura and M. Tohma,
Dynamic coexistence in a three-species competition–diffusion system, Ecological Complexity, 21 (2015), 215-232.
|
[22] |
H. L. Smith and P. Waltman,
Competition for a single limiting resource in continuous culture: the variable-yield model, SIAM J. Appl. Math., 54 (1994), 1113-1131.
doi: 10.1137/S0036139993245344. |





[1] |
Cheng-Hsiung Hsu, Ting-Hui Yang. Traveling plane wave solutions of delayed lattice differential systems in competitive Lotka-Volterra type. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 111-128. doi: 10.3934/dcdsb.2010.14.111 |
[2] |
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 |
[3] |
Anthony W. Leung, Xiaojie Hou, Wei Feng. Traveling wave solutions for Lotka-Volterra system re-visited. Discrete and Continuous Dynamical Systems - B, 2011, 15 (1) : 171-196. doi: 10.3934/dcdsb.2011.15.171 |
[4] |
Chiun-Chuan Chen, Li-Chang Hung. An N-barrier maximum principle for elliptic systems arising from the study of traveling waves in reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1503-1521. doi: 10.3934/dcdsb.2018054 |
[5] |
Chiun-Chuan Chen, Li-Chang Hung. Nonexistence of traveling wave solutions, exact and semi-exact traveling wave solutions for diffusive Lotka-Volterra systems of three competing species. Communications on Pure and Applied Analysis, 2016, 15 (4) : 1451-1469. doi: 10.3934/cpaa.2016.15.1451 |
[6] |
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 |
[7] |
Zhi-Cheng Wang, Hui-Ling Niu, Shigui Ruan. On the existence of axisymmetric traveling fronts in Lotka-Volterra competition-diffusion systems in ℝ3. Discrete and Continuous Dynamical Systems - B, 2017, 22 (3) : 1111-1144. doi: 10.3934/dcdsb.2017055 |
[8] |
Zengji Du, Shuling Yan, Kaige Zhuang. Traveling wave fronts in a diffusive and competitive Lotka-Volterra system. Discrete and Continuous Dynamical Systems - S, 2021, 14 (9) : 3097-3111. doi: 10.3934/dcdss.2021010 |
[9] |
Bang-Sheng Han, Zhi-Cheng Wang, Zengji Du. Traveling waves for nonlocal Lotka-Volterra competition systems. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1959-1983. doi: 10.3934/dcdsb.2020011 |
[10] |
Jian Fang, Jianhong Wu. Monotone traveling waves for delayed Lotka-Volterra competition systems. Discrete and Continuous Dynamical Systems, 2012, 32 (9) : 3043-3058. doi: 10.3934/dcds.2012.32.3043 |
[11] |
Jong-Shenq Guo, Ying-Chih Lin. The sign of the wave speed for the Lotka-Volterra competition-diffusion system. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2083-2090. doi: 10.3934/cpaa.2013.12.2083 |
[12] |
Jiang Liu, Xiaohui Shang, Zengji Du. Traveling wave solutions of a reaction-diffusion predator-prey model. Discrete and Continuous Dynamical Systems - S, 2017, 10 (5) : 1063-1078. doi: 10.3934/dcdss.2017057 |
[13] |
Bang-Sheng Han, Zhi-Cheng Wang. Traveling wave solutions in a nonlocal reaction-diffusion population model. Communications on Pure and Applied Analysis, 2016, 15 (3) : 1057-1076. doi: 10.3934/cpaa.2016.15.1057 |
[14] |
Xiaojie Hou, Yi Li. Local stability of traveling-wave solutions of nonlinear reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 681-701. doi: 10.3934/dcds.2006.15.681 |
[15] |
Tongren Ding, Hai Huang, Fabio Zanolin. A priori bounds and periodic solutions for a class of planar systems with applications to Lotka-Volterra equations. Discrete and Continuous Dynamical Systems, 1995, 1 (1) : 103-117. doi: 10.3934/dcds.1995.1.103 |
[16] |
Shaohua Chen, Runzhang Xu, Hongtao Yang. Global and blowup solutions for general Lotka-Volterra systems. Communications on Pure and Applied Analysis, 2016, 15 (5) : 1757-1768. doi: 10.3934/cpaa.2016012 |
[17] |
Yuzo Hosono. Traveling waves for the Lotka-Volterra predator-prey system without diffusion of the predator. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 161-171. doi: 10.3934/dcdsb.2015.20.161 |
[18] |
Yang Wang, Xiong Li. Uniqueness of traveling front solutions for the Lotka-Volterra system in the weak competition case. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3067-3075. doi: 10.3934/dcdsb.2018300 |
[19] |
Zhi-Xian Yu, Rong Yuan. Traveling wave fronts in reaction-diffusion systems with spatio-temporal delay and applications. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 709-728. doi: 10.3934/dcdsb.2010.13.709 |
[20] |
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 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]