Traveling Wave Solutions for Delayed Reaction–Diffusion Systems and Applications to Diffusive Lotka–Volterra Competition Models with Distributed Delays

By Guo Lin, Shigui Ruan. 2014

83 citations recorded by the source corpus.

This paper is concerned with the traveling wave solutions of delayed reaction–diffusion systems. By using Schauder’s fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and lower solutions. Using the technique of contracting rectangles, the asymptotic behavior of traveling wave solutions for delayed diffusive systems is obtained. To illustrate our main results, the existence, nonexistence and asymptotic behavior of positive traveling wave solutions of diffusive Lotka–Volterra competition systems with distributed delays are established. The existence of nonmonotone traveling wave solutions of diffusive Lotka–Volterra competition systems is also discussed. In particular, it is proved that if there exists instantaneous self-limitation effect, then the large delays appearing in the intra-specific competitive terms may not affect the existence and asymptotic behavior of traveling wave solutions.

Subfields: Computer Networks and Communications, Genetics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/6b9e4050ed025f9fd4151133324cf17fad8fdda4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

In Genetics

In Public Health, Environmental and Occupational Health

Citations in the corpus

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.”