一类具有余弦核的积分差分方程的分析
Analysis of a Class of Integrodifference Equations with Cosine Kernel
DOI: 10.12677/AAM.2022.1111815, PDF,    国家自然科学基金支持
作者: 范礼媛, 郭志明*：广州大学数学与信息科学学院，广东 广州
关键词: 捕食与被捕食模型；积分差分方程；稳定性；空间因素；余弦核；Predation-Prey Models； Integrodifference Equations； Stability； Spatial Factors； Cosine Kernel
摘要: 捕食与被捕食是经典的生态学种间关系，本文首先建立了一类世代重叠的离散时间捕食与被捕食模型并讨论了其不动点的稳定性。物种的空间扩散是普遍存在的，我们加入余弦核函数，建立了一类可以描述两个物种在空间中相互作用的积分差分方程模型，而这种无穷维离散时间空间扩散系统可以在余弦核下简化为有限维系统。我们分析了其与非空间模型对应的不动点稳定性并讨论了引入的空间参数对模型动力学的影响。最后通过数值分析验证了主要结论。
Abstract: Predation-prey are classical ecological interspecific relationships. In this paper, we first establish a class of discrete-time predation-prey models with overlapping generations and discuss the stability of their fixed points. The spatial diffusion of species is universal, and we incorporate cosine kernel functions to establish a class of integrodifference equations that can describe the interaction of two species in space, and this infinite-dimensional discrete-time spatial diffusion system can be reduced to a finite-dimensional system under the cosine kernel. We analyze its fixed point stability corre-sponding to the non-spatial model and discuss the effect of the introduced spatial parameters on the model dynamics. Finally, the main conclusions are verified by numerical analysis.
文章引用：范礼媛, 郭志明. 一类具有余弦核的积分差分方程的分析[J]. 应用数学进展, 2022, 11(11): 7696-7718. https://doi.org/10.12677/AAM.2022.1111815

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