Qualitative analysis of a diffusive prey-predator model with trophic interactions of three levels
Qualitative analysis of a diffusive prey-predator model with trophic interactions of three levels
复制标题
DOI：
10.3934/dcdsb.2012.17.127
复制
发表时间：
2011-10
影响因子：
1.2
通讯作者：
Huiling Li;P. Pang;Mingxin Wang
中科院分区：
文献类型：
--
作者：
Huiling Li;P. Pang;Mingxin Wang
本文考虑一类具有扩散和营养相互作用的三层食饵-捕食者动力系统的数学模型。在这个模型中，一般的营养函数之间的比例的猎物和捕食者的线性函数的基础上使用在每个级别。在这两个限制的营养功能，恢复经典的食饵依赖和比率依赖捕食模型，分别。我们提供了一个完整的讨论下的齐次诺依曼边界条件的模型的动力学行为（相同的行为也被视为在没有扩散）。在齐次Dirichlet边界条件下，讨论了平衡态正解的存在性、唯一性、稳定性和分支。最后，我们给出了这些结果在不同的捕食模型的背景下的解释。
In this paper, we consider a mathematical model for a prey-predator dynamical system with diffusion and trophic interactions of three levels. In this model, a general trophic function based on the ratio between the prey and a linear function of the predator is used at each level. At the two limits of this trophic function, one recovers the classical prey-dependent and ratio-dependent predation models, respectively. We offer a complete discussion of the dynamical behavior of the model under the homogeneous Neumann boundary condition (the same behavior is also seen in the absence of diffusion). We also discuss existence, uniqueness, stability and bifurcation of equilibrium behavior corresponding to positive steady state solutions under the homogeneous Dirichlet boundary condition. Finally, we give interpretations of some of these results in the context of different predation models.