# American Institute of Mathematical Sciences

June  2018, 15(3): 765-773. doi: 10.3934/mbe.2018034

## Analyzing the causes of alpine meadow degradation and the efficiency of restoration strategies through a mathematical modelling exercise

 1 Department of Applied Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, China 2 Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB E3B 5A3, Canada 3 North-West Plateau Institute of Biology, the Chinese Academy of Sciences, Key Laboratory of Ecology Restoration in Cold Region in Qinghai Province, Xining, Qinghai 810001, China

* Corresponding author

Received  May 20, 2017 Revised  September 11, 2017 Published  December 2017

Citation: Hanwu Liu, Lin Wang, Fengqin Zhang, Qiuying Li, Huakun Zhou. Analyzing the causes of alpine meadow degradation and the efficiency of restoration strategies through a mathematical modelling exercise. Mathematical Biosciences & Engineering, 2018, 15 (3) : 765-773. doi: 10.3934/mbe.2018034
##### References:

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##### References:
The stability regions of equilibria in the $C-A$ plane.
Bifurcation diagrams of Model (2) showing the globally stable equilibria only. Left: $C< \theta K$; Middle: $\theta K<C<K$; Right: $C>K$.
Variation of coordinates $x^{*}, y^{*}, z^{*}, u^{*}$ of $E_{5}$ and values of $A$, $\theta$ when one of the parameters $d_{1}, r, K, d_{3}, d_{4}, q$ increases (all other parameters are fixed).
 Parameter $d_{1}$ $r$ $K$ $d_{3}$ $d_{4}$ $q$ $x^{*}$ $-$ $-$ $-$ $\nearrow$ $-$ $-$ $y^{*}$ $-$ $-$ $-$ $-$ $\nearrow$ $\searrow$ $z^{*}$ $\searrow$ $-$ $-$ $-$ $\nearrow$ $\searrow$ $u^{*}$ $-$ $\nearrow$ $\nearrow$ $\searrow$ $\searrow$ $\nearrow$ $A$ $\nearrow$ $-$ $-$ $-$ $-$ $-$ $\theta$ $-$ $\nearrow$ $-$ $\searrow$ $-$ $-$
 Parameter $d_{1}$ $r$ $K$ $d_{3}$ $d_{4}$ $q$ $x^{*}$ $-$ $-$ $-$ $\nearrow$ $-$ $-$ $y^{*}$ $-$ $-$ $-$ $-$ $\nearrow$ $\searrow$ $z^{*}$ $\searrow$ $-$ $-$ $-$ $\nearrow$ $\searrow$ $u^{*}$ $-$ $\nearrow$ $\nearrow$ $\searrow$ $\searrow$ $\nearrow$ $A$ $\nearrow$ $-$ $-$ $-$ $-$ $-$ $\theta$ $-$ $\nearrow$ $-$ $\searrow$ $-$ $-$
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