论文标题
具有记忆效应和空间异质性的单人群模型的动力学
Dynamics of A Single Population Model with Memory Effect and Spatial Heterogeneity
论文作者
论文摘要
在本文中，考虑了具有记忆效应的单人群模型和配备诺伊曼边界的环境的异质性。空间非均匀稳态的全球存在通过上和下溶液的方法证明，这对于相对较小的记忆扩散是渐近稳定的。但是，在记忆的扩散率超过临界值之后，如果域内内在生长速率的积分是负面的，则可以通过HOPF分叉生成空间不均匀的周期性解决方案。如果只提出了记忆的扩散或空间异质性，则将永远不会发生这种现象，因此必须由它们的关节效应诱导。这表明记忆的扩散将在整体敌对环境中带来时空模式。当域上的内在增长率的积分为正时，事实证明稳态仍然渐近稳定。最后，如果边界条件被Dirichlet条件取代，则还讨论了模型的可能动力学。
In this paper, a single population model with memory effect and the heterogeneity of the environment, equipped with the Neumann boundary, is considered. The global existence of a spatial nonhomogeneous steady state is proved by the method of upper and lower solutions, which is asymptotically stable for relatively small memorized diffusion. However, after the memorized diffusion rate exceeding a critical value, spatial inhomogeneous periodic solution can be generated through Hopf bifurcation, if the integral of intrinsic growth rate over the domain is negative. Such phenomenon will never happen, if only memorized diffusion or spatially heterogeneity is presented, and therefore must be induced by their joint effects. This indicates that the memorized diffusion will bring about spatial-temporal patterns in the overall hostile environment. When the integral of intrinsic growth rate over the domain is positive, it turns out that the steady state is still asymptotically stable. Finally, the possible dynamics of the model is also discussed, if the boundary condition is replaced by Dirichlet condition.
