EAPSI:Developing periodic life cycles through interspecies competition

许多植物和动物都有种群周期；然而，这些周期的原因通常是未知的。例如，虽然美国有13年和17年的蝉，每13年或17年在其种群中出现周期性爆发，但日本的蝉每年夏天都很流行，没有这种周期性。了解种群周期对于管理渔业和农作物、保护濒危物种以及处理物种入侵和流行病传播具有重要意义。在本研究中，周期性生命周期的原因将通过两个竞争种群的模型进行调查。在隔离时，种群不会出现周期性暴发；然而，当它们在一起时，它们之间的相互作用导致两者都出现周期性爆发，类似于在美国东部发现的著名的13年和17年蝉。这项研究将在日本宫崎大学与人口动态周期性的主要研究员Ryusuke Kon教授一起进行。离散时间矩阵模型的平衡和循环及其稳定性将首先通过数值探索，然后通过解析来确定。还将对系统进行分岔分析，以确定动力学对模型参数的依赖关系。除了基本的线性稳定性分析，一些具体的分析方法可能包括使用李雅普诺夫函数，李雅普诺夫-施密特约简，和/或中心流形理论。模型的动力学，特别是与自然界中可能发现的现象相对应的稳定平衡，将与现有的生物体联系起来。NSF EAPSI奖是与日本科学促进会合作资助的。

Population cycles occur in many plants and animals; however the causes of these cycles are usually unknown. For example, although there are 13- and 17-year cicadas in the United States which exhibit periodic outbreaks in their populations every 13 or 17 years, cicadas in Japan are prevalent every summer and lack such periodicity. The understanding of population cycles is important to managing fisheries and crops, protecting endangered species, and dealing with species invasions and the spread of epidemics. In this research, the causes of periodic life cycles will be investigated through a model of two competing populations. When isolated, the populations do not exhibit periodic outbreaks; however, when together, the interactions between them cause both to develop periodic outbreaks similar to those of the famous 13- and 17-year cicadas found in the eastern United States. This research will be done at the University of Miyazaki in Japan with Professor Ryusuke Kon, a leading researcher of periodicity in population dynamics.The equilibria and cycles of the discrete-time matrix model and their stabilities will be determined, first through numerical exploration and then analytically. A bifurcation analysis of the system will also be done to determine dynamics' dependence on the model parameters. In addition to a basic linear stability analysis, some specific methods of analysis may include using Lyapunov functions, the Lyapunov-Schmidt reduction, and/or center-manifold theory. The dynamics of the model, particularly the stable equilibria which correspond to phenomena likely to be found in nature, will then be related to existing organisms. This NSF EAPSI award is funded in collaboration with the Japan Society for the Promotion of Science.