Traveling wave solutions to a cubic predator-prey diffusion model with stage structure for the prey

Yujuan Jiao; Jinmiao Yang; Hang Zhang; Yujuan Jiao; Jinmiao Yang; Hang Zhang

doi:10.3934/math.2022888

AIMS Mathematics

2022, Volume 7, Issue 9: 16261-16277. doi: 10.3934/math.2022888

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Research article

Traveling wave solutions to a cubic predator-prey diffusion model with stage structure for the prey

College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou, 730030, China

Received: 20 April 2022 Revised: 14 June 2022 Accepted: 20 June 2022 Published: 04 July 2022
MSC : 34C37, 35C07

In this paper, we investigate the traveling wave solutions to a cubic predator-prey diffusion model with stage structure for the prey. Firstly, using the upper and lower solutions method we prove the existence and non-existence of weak traveling wave solutions. Furthermore, we prove that the weak traveling wave solutions are actually traveling wave solutions under additional conditions by using Lyapunov function method and LaSalle's invariance principle.
- predator-prey model,
- traveling wave solution,
- upper and lower solution,
- Lyapunov function,
- LaSalle's invariance principle
Citation: Yujuan Jiao, Jinmiao Yang, Hang Zhang. Traveling wave solutions to a cubic predator-prey diffusion model with stage structure for the prey[J]. AIMS Mathematics, 2022, 7(9): 16261-16277. doi: 10.3934/math.2022888

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Abstract

In this paper, we investigate the traveling wave solutions to a cubic predator-prey diffusion model with stage structure for the prey. Firstly, using the upper and lower solutions method we prove the existence and non-existence of weak traveling wave solutions. Furthermore, we prove that the weak traveling wave solutions are actually traveling wave solutions under additional conditions by using Lyapunov function method and LaSalle's invariance principle.

References

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