Qualitative analysis and traveling wave solutions of a predator-prey model with time delay and stage structure

Meng Wang; Naiwei Liu; Meng Wang; Naiwei Liu

doi:10.3934/era.2024121

Electronic Research Archive

2024, Volume 32, Issue 4: 2665-2698. doi: 10.3934/era.2024121

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Qualitative analysis and traveling wave solutions of a predator-prey model with time delay and stage structure

Meng Wang ,
Naiwei Liu ^,

School of Mathematics and Information Science, Yantai University, Yantai 264000, China

Received: 17 January 2024 Revised: 23 February 2024 Accepted: 19 March 2024 Published: 01 April 2024

In this paper, we considered a delayed predator-prey model with stage structure and Beddington-DeAngelis type functional response. First, we analyzed the stability of the constant equilibrium points of the model by the linear stability method. Furthermore, we considered the existence of traveling wave solutions connecting the zero equilibrium point and the unique positive equilibrium point. Second, we transformed the existence of traveling wave solutions into the existence of fixed points of an operator by constructing suitable upper and lower solutions, and combined with the Schauder fixed point theorem, we gave the existence of fixed points and obtained the existence of traveling wave solutions of the model.
- predator-prey model,
- stage structure,
- time delay,
- upper-lower solutions,
- traveling wave solution
Citation: Meng Wang, Naiwei Liu. Qualitative analysis and traveling wave solutions of a predator-prey model with time delay and stage structure[J]. Electronic Research Archive, 2024, 32(4): 2665-2698. doi: 10.3934/era.2024121

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Abstract

In this paper, we considered a delayed predator-prey model with stage structure and Beddington-DeAngelis type functional response. First, we analyzed the stability of the constant equilibrium points of the model by the linear stability method. Furthermore, we considered the existence of traveling wave solutions connecting the zero equilibrium point and the unique positive equilibrium point. Second, we transformed the existence of traveling wave solutions into the existence of fixed points of an operator by constructing suitable upper and lower solutions, and combined with the Schauder fixed point theorem, we gave the existence of fixed points and obtained the existence of traveling wave solutions of the model.

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