Multiple positive periodic solutions of a Gause-type predator-prey model with Allee effect and functional responses

Shanshan Yu; Jiang Liu; Xiaojie Lin; Shanshan Yu; Jiang Liu; Xiaojie Lin

doi:10.3934/math.2020394

AIMS Mathematics

2020, Volume 5, Issue 6: 6135-6148. doi: 10.3934/math.2020394

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Multiple positive periodic solutions of a Gause-type predator-prey model with Allee effect and functional responses

1.
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China
2.
Nanjing No. 29 High School, Nanjing, Jiangsu 210036, China

Received: 23 June 2020 Accepted: 20 July 2020 Published: 29 July 2020
MSC : 34C25; 92D25

This paper deals with a Gause-type predator-prey model with Allee effect and Holling type III functional response. We also consider the influence of predator competition and the artificial harvesting on predator-prey system. The existence of multiple positive periodic solutions of the predator-prey model is established by using the Mawhin coincidence degree theory.
- predator-prey model,
- Allee effect,
- functional response,
- harvesting term,
- periodic solutions,
- Mawhin coincidence degree
Citation: Shanshan Yu, Jiang Liu, Xiaojie Lin. Multiple positive periodic solutions of a Gause-type predator-prey model with Allee effect and functional responses[J]. AIMS Mathematics, 2020, 5(6): 6135-6148. doi: 10.3934/math.2020394

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Abstract

This paper deals with a Gause-type predator-prey model with Allee effect and Holling type III functional response. We also consider the influence of predator competition and the artificial harvesting on predator-prey system. The existence of multiple positive periodic solutions of the predator-prey model is established by using the Mawhin coincidence degree theory.

References

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