In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an aperiodic influence on the models leading to nonautonomous integrodifference equations. In order to capture their long-term behaviour comprehensively, both pullback and forward attractors, as well as forward limit sets are constructed for general infinite-dimensional nonautonomous dynamical systems in discrete time. While the theory of pullback attractors, but not their application to integrodifference equations, is meanwhile well-established, the present novel approach is needed in order to understand their future behaviour.

在理论生态学中，描述具有非重叠世代的物种的空间扩散和时间演化的模型通常基于积分差异方程。对于各种此类应用，环境对导致非自治积分差方程的模型具有非周期性影响。为了全面捕捉它们的长期行为，在离散时间为一般无限维非自治动力系统构建了前向和后向吸引子以及前向极限集。虽然回拉吸引子的理论，但不是它们在积分差方程中的应用，同时得到了很好的确立，但需要目前的新方法来理解它们未来的行为。