@article{Liu2025, 
author = {Qi Liu and Yujuan Jiao},
title = {Traveling wave solutions to a one prey-two competing predators model with nonlocal delay},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {21693-21720},
keywords = {one prey-two competing predators model, nonlocal delay, traveling wave solutions, Lyapunov function, cross-iteration},
url = {https://www.sciopen.com/article/10.3934/math.2025964},
doi = {10.3934/math.2025964},
abstract = {In this paper, we investigated the traveling wave solutions to a one prey-two competing predators model with nonlocal delay. First, we analyzed the stability of the positive equilibrium by using a Lyapunov function. Then, by examining the distribution of the roots of the characteristic equation, we ascertained the critical wave speed        c    ∗  . Finally, employing the cross iteration method and Schauder's fixed point theorem, we proved the existence of traveling wave solutions connecting the trivial equilibrium    (  0  ,  0  ,  0  ) with the positive equilibrium    (      u    ∗    ,      v    ∗    ,      w    ∗    ) for wave speeds    c  >      c    ∗  . The incorporation of nonlocal delay into models featuring intra-specific and inter-specific competition significantly elevates computational complexity, thereby necessitating precise analytical estimates.}
}