A PREY-PREDATOR MODEL WITH HOLLING Ⅱ FUNCTIONAL RESPONSE AND THE CARRYING CAPACITY OF PREDATOR DEPENDING ON ITS PREY

Hanwu Liu; Ting Li; Fengqin Zhang

doi:10.11948/2018.1464

2018 Volume 8 Issue 5

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Hanwu Liu, Ting Li, Fengqin Zhang. A PREY-PREDATOR MODEL WITH HOLLING Ⅱ FUNCTIONAL RESPONSE AND THE CARRYING CAPACITY OF PREDATOR DEPENDING ON ITS PREY[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1464-1474. doi: 10.11948/2018.1464

Citation:

Hanwu Liu, Ting Li, Fengqin Zhang. A PREY-PREDATOR MODEL WITH HOLLING Ⅱ FUNCTIONAL RESPONSE AND THE CARRYING CAPACITY OF PREDATOR DEPENDING ON ITS PREY[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1464-1474. doi: 10.11948/2018.1464

A PREY-PREDATOR MODEL WITH HOLLING Ⅱ FUNCTIONAL RESPONSE AND THE CARRYING CAPACITY OF PREDATOR DEPENDING ON ITS PREY

1 Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, China;
2 School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China

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Abstract

Abstract

One prey-predator model is formulated and the global behavior of its solution is analyzed. In this model, the carrying capacity of predator depends on the amount of its prey, and the Holling Ⅱ functional response is involved. This model may have four classes of positive equilibriums and limit cycle. The positive equilibriums may be stable, or a saddle-node, or a saddle, or a degenerate singular point. In alpine meadow ecosystem, the dynamics of vegetation and plateau pika can be described by this model. Through simulating with virtual parameters, the cause of alpine meadow degradation and effective recovery strategy is investigated. Increasing grazing rate or decreasing plateau pika mortality may cause alpine meadow degradation. Correspondingly, reducing grazing rate and increasing plateau pika mortality may recover the degraded alpine meadow effectively.
- Prey-predator model /
- density-dependent /
- global behavior /
- Holling Ⅱ functional response
MSC: 34D20;34C60;92D25

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References

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