Electron. J. Differential Equations,
Vol. 2019 (2019), No. 34, pp. 119.
Qualitative properties of traveling wavefronts for a
threecomponent lattice dynamical system with delay
Pei Gao, Shi Liang Wu
Abstract:
This article concerns a threecomponent delayed lattice dynamical system
arising in competition models. In such models, traveling wave solutions
serve an important tool to understand the competition mechanism,
i.e. which species will survive or die out eventually.
We first prove the existence of the minimal wave speed of the
traveling wavefronts connecting two equilibria (1,0,1) and (0,1,0).
Then, for sufficiently small intraspecific competitive delays, we
establish the asymptotic behavior of the traveling wave solutions at
minus/plus infinity. Finally the strict monotonicity and uniqueness of
all traveling wave solutions are obtained for the case where intraspecific
competitive delays are zeros. In particular, the effect of the delays on
the minimal wave speed and the decay rate of the traveling profiles at
minus/plus infinity is also investigated.
Submitted July 8, 2018. Published February 25, 2019.
Math Subject Classifications: 35B40, 35R10, 37L60, 58D25.
Key Words: Delayed lattice competitive system; traveling wave solution;
asymptotic behavior; monotonicity; uniqueness.
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Pei Gao
School of Mathematics and Statistics
Xidian University
Xi'an, Shaanxi 710071, China
email: 291435148@qq.com


Shi Liang Wu
School of Mathematics and Statistics
Xidian University
Xi'an, Shaanxi 710071, China
email: slwu@xidian.edu.cn

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