EAPSI:Developing periodic life cycles through interspecies competition

种群周期发生在许多植物和动物身上；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，它们的种群每13或17年就会周期性地爆发一次，但在日本，蝉在每年夏天都很普遍，没有这样的周期性。对种群周期的了解对于管理渔业和农作物、保护濒危物种以及应对物种入侵和流行病传播非常重要。在这项研究中，将通过两个竞争种群的模型来研究周期性生命周期的原因。当被隔离时，这些种群不会表现出周期性的爆发；然而，当它们在一起时，它们之间的相互作用会导致两者产生类似于在美国东部发现的著名的13年和17年蝉的周期性爆发。这项研究将在日本宫崎大学与人口动力学周期研究的领军人物今龙介教授一起完成。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，然后通过分析来确定。还将对系统进行分叉分析，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外，一些具体的分析方法可能包括使用Lyapunov函数、Lyapunov-Schmidt约化和/或中心流形理论。该模型的动力学，特别是与可能在自然界中发现的现象相对应的稳定平衡，将与现有的有机体有关。该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.