Traveling wave solutions in delayed reaction diffusion systems with applications to multi-species models
By Guo Lin, Wan-Tong Li, Ming Ma. 2009
77 citations recorded by the source corpus.
This paper is concerned with the existence of traveling wave solutions in delayed reaction diffusion systems which at least contain multi-species competition, cooperation and predator-prey models with diffusion and delays. By introducing the mixed quasimonotone condition and the exponentially mixed quasimonotone condition, we reduce the existence of traveling wave solutions to the existence of a pair of admissible upper-lower solutions. To illustrate our main results, the existence of traveling wave solutions of multi-species competition, cooperation and predator-prey Lotka-Volterra systems with delays is considered. In particular, we show the precisely asymptotic behavior of the traveling wave solutions of these Lotka-Volterra systems.
Subfields: Computer Networks and Communications, Genetics, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/cda3e887777ceb4799093bbcc921b8186d279bfc
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In Computer Networks and Communications
In Genetics
In Public Health, Environmental and Occupational Health
Citations in the corpus
- Asymptotic spreading of competition diffusion systems: The role of interspecific competitions (2012, background): “Due to the special form and asymptotic boundary conditions of travelling wave solutions in [1, 25, 27, 34, 43], it is clear that these travelling wave solutions represent the spatial invasion process from one unbounded domain to another.”
- Traveling wave solutions for a continuous and discrete diffusive predator–prey model (2017, background): “For this aspect, we refer the reader to the works [23, 17, 18, 21, 15, 19, 22] for the continuous case and [16, 20] for the discrete case.”
- On some Free Boundary Problems of the Prey-predator Model (2013, background): “17 of [20] still holds for the traveling wave fronts of the following system”