Periodic solution of a stage-structured predator-prey model with Crowley-Martin type functional response

Weijie Lu; Yonghui Xia; Weijie Lu; Yonghui Xia

doi:10.3934/math.2022454

AIMS Mathematics

2022, Volume 7, Issue 5: 8162-8175. doi: 10.3934/math.2022454

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Research article

Periodic solution of a stage-structured predator-prey model with Crowley-Martin type functional response

Weijie Lu ,
Yonghui Xia ^,

Department of Mathematics, Zhejiang Normal University, 321004, Jinhua, China

Received: 22 December 2021 Revised: 10 February 2022 Accepted: 16 February 2022 Published: 25 February 2022
MSC : 34C25, 92B05, 92D25

In this paper, the existence of positive periodic solution of stage-structured predator-prey model with Crowley-Martin type functional response is investigated. The prey population fall into two categories: mature and immature prey. The predator population is dependent only on mature prey and is influenced by Crowley-Martin type functional response. Based on the Mawhin's coincidence degree theory and nontrivial estimation techniques for a priori bounds of unknown solutions to the operator equation $ Fz = \mu Nz $, we prove the existence of positive periodic solution. Finally, the effectiveness of our result is verified by an example and numerical simulation.
- periodic solution,
- stag-structure,
- Crowley-Martin type functional response
Citation: Weijie Lu, Yonghui Xia. Periodic solution of a stage-structured predator-prey model with Crowley-Martin type functional response[J]. AIMS Mathematics, 2022, 7(5): 8162-8175. doi: 10.3934/math.2022454

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Abstract

In this paper, the existence of positive periodic solution of stage-structured predator-prey model with Crowley-Martin type functional response is investigated. The prey population fall into two categories: mature and immature prey. The predator population is dependent only on mature prey and is influenced by Crowley-Martin type functional response. Based on the Mawhin's coincidence degree theory and nontrivial estimation techniques for a priori bounds of unknown solutions to the operator equation $ Fz = \mu Nz $, we prove the existence of positive periodic solution. Finally, the effectiveness of our result is verified by an example and numerical simulation.

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