Stability and co-existence state traveling wave solution for a general N-dimensional diffusive delayed Lotka-Volterra equation in a cylinder.

A general |$N$| -dimensional non-monotone delayed diffusive Lotka–Volterra model is considered in our paper. First, we obtain the global stability of the model subject to Neumann boundary condition by using a small delay result for delayed systems. Second, the limits at |$+\infty $| of bounded travelling wave solutions are confirmed by virtue of such global stability. Therefore, the existence of co-existence state travelling wave solutions is established. Finally, an example is given to illustrate the biological significance of the assumptions in the current paper. [ABSTRACT FROM AUTHOR]