Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong.
Math Biosci Eng. 2021 Aug 9;18(5):6672-6699. doi: 10.3934/mbe.2021331.
We study the existence of global unique classical solution to a density-dependent prey-predator population system with indirect prey-taxis effect. With two Lyapunov functions appropriately constructed, we then show that the solution can asymptotically approach prey-only state or coexistence state of the system under suitable conditions. Moreover, linearized analysis on the system at these two constant steady states shows their linear instability criterion. By numerical simulation we find that some density-dependent prey-taxis and predators' diffusion may either flatten the spatial one-dimensional patterns which exist in non-density-dependent case, or break the spatial two-dimensional distribution similarity which occurs in non-density-dependent case between predators and chemoattractants (released by prey).
我们研究了一类具有间接食饵趋向效应的密度依赖型食饵-捕食者种群系统整体古典解的存在性。通过适当构造两个李雅普诺夫函数，我们证明在合适的条件下，解可以渐近地趋近于系统的纯食饵状态或共存状态。此外，在这两个常数稳态下对系统进行线性化分析，得到了它们的线性不稳定性判据。通过数值模拟，我们发现某些密度依赖型食饵趋向和捕食者扩散可能会使非密度依赖型情况下存在的一维空间模式变平，或者打破非密度依赖型情况下捕食者和化感物质（由食饵释放）之间的二维空间分布相似性。
