Traveling wave solutions to a one prey-two competing predators model with nonlocal delay

Qi Liu; Yujuan Jiao; Qi Liu; Yujuan Jiao

doi:10.3934/math.2025964

AIMS Mathematics

2025, Volume 10, Issue 9: 21693-21720. doi: 10.3934/math.2025964

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Research article

Traveling wave solutions to a one prey-two competing predators model with nonlocal delay

Qi Liu ,
Yujuan Jiao ^,

College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730124, China

Received: 04 July 2025 Revised: 08 September 2025 Accepted: 12 September 2025 Published: 18 September 2025
MSC : 34C37, 35C07

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.
- one prey-two competing predators model,
- nonlocal delay,
- traveling wave solutions,
- Lyapunov function,
- cross-iteration
Citation: Qi Liu, Yujuan Jiao. Traveling wave solutions to a one prey-two competing predators model with nonlocal delay[J]. AIMS Mathematics, 2025, 10(9): 21693-21720. doi: 10.3934/math.2025964

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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.

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