Integrodifference equations are versatile models in theoretical ecology for the spatial dispersal of species evolving in non-overlapping generations. The dynamics of these infinite-dimensional discrete dynamical systems is often illustrated using computational simulations. This paper studies the effect of Nyström discretization to the local dynamics of periodic integrodifference equations having Hölder continuous functions over a compact domain as state space. We prove persistence and convergence for hyperbolic periodic solutions and their associated stable and unstable manifolds respecting the convergence order of the quadrature/cubature method.

中文翻译：

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积分差分方程的数值动力学

积分差分方程是理论生态学中用于在非重叠世代中进化的物种空间扩散的通用模型。这些无限维离散动力系统的动力学通常使用计算模拟来说明。本文研究了 Nyström 离散化对在作为状态空间的紧域上具有 Hölder 连续函数的周期性积分差分方程的局部动力学的影响。我们证明了双曲周期解的持久性和收敛性及其相关的稳定和不稳定流形关于正交/立方体方法的收敛顺序。