Sarwardi Sahabuddin, Mandal Prashanta Kumar, Ray Santanu
Department of Mathematics, Aliah University, DN-41, Sector-V, Salt Lake City, Kolkata 700 091, West Bengal, India.
J Biol Phys. 2013 Sep;39(4):701-22. doi: 10.1007/s10867-013-9327-7. Epub 2013 Aug 23.
A three-component model consisting on one-prey and two-predator populations is considered with a Holling type II response function incorporating a constant proportion of prey refuge. We also consider the competition among predators for their food (prey) and shelter. The essential mathematical features of the model have been analyzed thoroughly in terms of stability and bifurcations arising in some selected situations. Threshold values for some parameters indicating the feasibility and stability conditions of some equilibria are determined. The range of significant parameters under which the system admits different types of bifurcations is investigated. Numerical illustrations are performed in order to validate the applicability of the model under consideration.
考虑一个由一个猎物种群和两个捕食者种群组成的三分量模型，其具有包含恒定比例猎物避难所的Holling II型响应函数。我们还考虑了捕食者之间对食物（猎物）和庇护所的竞争。已根据某些选定情况下出现的稳定性和分岔对该模型的基本数学特征进行了深入分析。确定了一些参数的阈值，这些阈值表明了某些平衡点的可行性和稳定性条件。研究了系统允许不同类型分岔的重要参数范围。进行了数值例证以验证所考虑模型的适用性。
