Dynamics of a non-autonomous predator-prey system with Hassell-Varley-Holling Ⅱ function response and mutual interference

Luoyi Wu; Hang Zheng; Songchuan Zhang; Luoyi Wu; Hang Zheng; Songchuan Zhang

doi:10.3934/math.2021355

AIMS Mathematics

2021, Volume 6, Issue 6: 6033-6049. doi: 10.3934/math.2021355

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Research article

Dynamics of a non-autonomous predator-prey system with Hassell-Varley-Holling Ⅱ function response and mutual interference

Department of Mathematics and Computer, Wuyi University, Wu Yishan, Fujian 354300, China

Received: 20 January 2021 Accepted: 19 March 2021 Published: 01 April 2021
MSC : 34K25, 34C27, 34D20, 92D25

In this paper, we establish a non-autonomous Hassell-Varley-Holling type predator-prey system with mutual interference. We construct some sufficient conditions for the permanence, extinction and globally asymptotic stability of system by use of the comparison theorem and an appropriate Liapunov function. Then the sufficient and necessary conditions for a periodic solution of the system are obtained via coincidence degree theorem. Finally, the correctness of the previous conclusions are demonstrated by some numerical cases.
- periodic solution,
- permanence,
- coincidence degree,
- globally asymptotic stability,
- numerical simulation
Citation: Luoyi Wu, Hang Zheng, Songchuan Zhang. Dynamics of a non-autonomous predator-prey system with Hassell-Varley-Holling Ⅱ function response and mutual interference[J]. AIMS Mathematics, 2021, 6(6): 6033-6049. doi: 10.3934/math.2021355

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Abstract

In this paper, we establish a non-autonomous Hassell-Varley-Holling type predator-prey system with mutual interference. We construct some sufficient conditions for the permanence, extinction and globally asymptotic stability of system by use of the comparison theorem and an appropriate Liapunov function. Then the sufficient and necessary conditions for a periodic solution of the system are obtained via coincidence degree theorem. Finally, the correctness of the previous conclusions are demonstrated by some numerical cases.

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