Existence of Traveling Waves of Lotka Volterra Type Models with Delayed Diffusion Term and Partial Quasimonotonicity

TL;DR

This paper proves the existence of traveling wave solutions in delayed two-species Lotka-Volterra models with non-monotonic interactions, using advanced fixed point and iteration methods.

Contribution

It extends the partial quasi-monotone iteration method to systems with delays and non-monotonicity, employing Schauder's fixed point theorem.

Findings

Existence of traveling wave solutions established for delayed Lotka-Volterra systems.

Extension of iteration methods to non-monotone, delayed reaction-diffusion systems.

Application of Schauder's fixed point theorem in this context.

Abstract

This paper is concerned with the existence of traveling wave solutions for diffusive two-species Lotka-Volterra systems with delay in both the reaction and diffusion terms without monotonicity. We extend the partial or cross monotone iteration method to systems that satisfy the partial quasi-monotone condition via construction appropriate upper and lower solutions. This is done by using Schauder's fixed point theorem.