Immunology Group, International Centre for Genetic Engineering and Biotechnology, Aruna Asaf Ali Marg, New Delhi 110067, India.
Math Biosci. 2012 Jul;238(1):1-11. doi: 10.1016/j.mbs.2012.04.002. Epub 2012 Apr 24.
A three dimensional nutrient-plant-herbivore model was proposed and conditions for boundedness, positive invariance, existence and stability of different equilibrium points, Hopf-bifurcation and global stability were obtained. We performed numerical simulations to observe the simultaneous effect of the top-down and the bottom-up mechanism on the system. It was found that nutrient enrichment destroyed the coexistence steady state of the system. This nutrient enrichment could be due to high nutrient input rate or high nutrient recycling rate. In both cases the system showed instability. Moreover, these results were independent of the grazing pressure and the predation functional form.
提出了一个三维的营养-植物-食草动物模型，得到了不同平衡点的有界性、正不变性、存在性和稳定性、Hopf 分支和全局稳定性的条件。我们进行了数值模拟，以观察自上而下和自下而上的机制对系统的同时影响。结果发现，营养富集破坏了系统的共存稳定状态。这种营养富集可能是由于高营养输入率或高营养再循环率造成的。在这两种情况下，系统都表现出不稳定性。此外，这些结果与放牧压力和捕食功能形式无关。
