Haque Mainul
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
Bull Math Biol. 2009 Feb;71(2):430-52. doi: 10.1007/s11538-008-9368-4. Epub 2008 Dec 13.
Ratio-dependent predator-prey models are increasingly favored by both the theoretical and experimental ecologists as a more suitable alternative to describe predator-prey interactions when the predators hunt seriously. In this article, the classical Bazykin's model is modified with ratio-dependent functional response. Stability and bifurcation situations of the system are observed. Since the ratio-dependent model always has difficult dynamics in the vicinity of the origin, the analytical behavior of the system near origin is studied completely. It is found that paradox of enrichment can happen to this system under certain parameter values, although the functional response is ratio-dependent. The parametric space for Turing spatial structure is determined. We also conclude that competition among the predator population might be beneficial for predator species under certain circumstances. Finally, ecological interpretations of our results are presented in the discussion section.
比率依赖型捕食者 - 猎物模型越来越受到理论生态学家和实验生态学家的青睐，因为当捕食者进行高强度捕食时，它是描述捕食者 - 猎物相互作用的更合适选择。在本文中，经典的巴齐金模型通过比率依赖型功能反应进行了修正。观察了该系统的稳定性和分岔情况。由于比率依赖型模型在原点附近总是具有复杂的动力学，因此对系统在原点附近的解析行为进行了全面研究。结果发现，尽管功能反应是比率依赖型的，但在某些参数值下，该系统仍可能出现富集悖论。确定了图灵空间结构的参数空间。我们还得出结论，在某些情况下，捕食者种群之间的竞争可能对捕食者物种有益。最后，在讨论部分给出了我们结果的生态学解释。
