Traveling wave fronts in a delayed lattice competitive system |
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Authors: | Kun Li Jianhua Huang Xiong Li Yanli He |
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Affiliation: | 1. School of Mathematics and Computational Science, Hunan First Normal University, Changsha, People’s Republic of China.;2. College of Science, National University of Defense Technology, Changsha, People’s Republic of China.;3. School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, People’s Republic of China. |
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Abstract: | This paper is concerned with the existence, asymptotic behavior, strict monotonicity, and uniqueness of traveling wave fronts connecting two half-positive equilibria in a delayed lattice competitive system. We first prove the existence of traveling wave fronts by constructing upper and lower solutions and Schauder’s fixed point theorem, and then, for sufficiently small intraspecific competitive delays, prove that these traveling wave fronts decay exponentially at both infinities. Furthermore, for system without intraspecific competitive delays, the strict monotonicity and uniqueness of traveling wave fronts are established by means of the sliding method. In addition, we give the exact decay rate of the stronger competitor under some technique conditions by appealing to uniqueness. |
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Keywords: | Delayed lattice competitive system traveling wave front asymptotic behavior uniqueness upper and lower solutions |
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