论文标题
$ c（ω）$ i的周期性集成差方程中的分叉：分析结果和应用
Bifurcations in periodic integrodifference equations in $C(Ω)$ I: Analytical results and applications
论文作者
论文摘要
我们研究了紧凑型栖息地周期性解决方案的周期性解决方案的局部分叉。这种无限维离散动力学系统在理论生态学中出现，作为描述具有非重叠世代的物种的空间分散的模型。 我们的明确标准使我们能够识别褶皱和交叉曲线类型的分支，其中包括经典的跨批评，干草叉和flip-scenario作为特殊情况。确实，不仅可以检测模型中的定性变化的工具。提供了空间生态学和相关的模拟，但是这些关键过渡也被分类。此外，研究和说明了各种时间周期性整合差方程的分叉行为。这需要基于所涉及的积分运算符的NyStröm离散化的分析方法和数值工具的组合。
We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the spatial dispersal of species having nonoverlapping generations. Our explicit criteria allow us to identify branchings of fold- and crossing curve-type, which include the classical transcritical-, pitchfork- and flip-scenario as special cases. Indeed, not only tools to detect qualitative changes in models from e.g. spatial ecology and related simulations are provided, but these critical transitions are also classified. In addition, the bifurcation behavior of various time-periodic integrodifference equations is investigated and illustrated. This requires a combination of analytical methods and numerical tools based on Nyström discretization of the integral operators involved.
