| Citation: |
Hanwu Liu, Fengqin Zhang, Huakun Zhou. THE DYNAMICAL BEHAVIOR AND APPLICATION OF ONE ALPINE MEADOW MODEL[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 2701-2712. doi: 10.11948/20200313
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THE DYNAMICAL BEHAVIOR AND APPLICATION OF ONE ALPINE MEADOW MODEL
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Abstract
In recent years, the alpine meadow has degraded seriously, before restoring the degraded alpine meadow, it is necessary to know the cause of degrading and to find the effective restoration measure. One forage grass-livestock-rodent-raptor dynamical model is formulated and analyzed. Based on this model, the cause of alpine meadow degrading is analyzed, the efficiency of restoration measures is evaluated. Overgrazing and uncontrolled hunting are the causes of alpine meadow degradation, and may lead to more serious disaster. Long time supplementary feeding aggravates alpine meadow degrading further. Climate change is not the unique cause of alpine meadow degradation at least. Both determining livestock number by grass yield together with controlling rodent with natural enemy and ecological resettlement together with controlling rodent with natural enemy are effective strategies of restoring degraded alpine meadow. Human beings should fully understand the consequence of their behavior, regulate their behavior, make human beings and nature develop harmoniously.
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Keywords:
- Dynamical model /
- alpine meadow /
- cause of degradation /
- restoration measure
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References
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Hanwu Liu, Fengqin Zhang, Huakun Zhou. THE DYNAMICAL BEHAVIOR AND APPLICATION OF ONE ALPINE MEADOW MODEL[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 2701-2712. doi: 10.11948/20200313
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Figure 1. The stability domains of equilibriums in
$ B - C $ plane. Where$ a = K(1 - AD) - \delta, b = K(1 - AD), c = K - \delta $ ($ c $ may be less than$ b $ , and$ a $ may be less than 0). -
Figure 2. The limit cycle and trajectories near it in plane
$ x - y $ . Where the values of parameters are$ r = 2.3year^{-1}, K = 100Kg, \delta = 50Kg, \alpha = 10Kg\cdot head^{-1}\cdot year^{-1}, \beta = 4.3year^{-1}, \mu = 0.01head^{-1}\cdot year^{-1}, $ $ \eta = 0.01Kg^{-1}\cdot year^{-1}, p = 0.02head^{-1}\cdot year^{-1}, q = 0.01head^{-1}\cdot year^{-1}, d_{2} = 1.2year^{-1}, d_{3} = 0.3year^{-1}, d_{4} = 0.5year^{-1}$ .