U.S.Bulgaria Cooperative Research Analytical and Computational Studies of Oscillations in Age-structured Population Models

小行星9412284 这笔赠款用于支持亚拉巴马大学亨茨维尔分校数学科学系的李佳博士和马克·J·弗里德曼博士以及保加利亚索菲亚科学院数学研究所数值方法实验室的坦尼娅·科斯托娃博士之间的一项美国-保加利亚联合合作研究项目“随机结构人口模型中振荡的分析和计算研究”。 研究的主题将包括年龄结构人口模型中振荡的分析和计算研究。 该研究的结果预计将在数学和生物科学方面产生影响，因为其主要目标是揭示单个种群规模的可能（并且经常在自然界中观察到）振荡行为的潜在机制。 理解这种机制是种群动力学理论中最重要的问题之一。 这项合作将使双方受益，因为参与研究的研究人员在处理此类模型方面有着密切但不同和互补的经验。 研究的重点是年龄结构模型线性化的谱分析，这是一个非线性偏微分-积分方程，其简化的各种形式，如常微分方程和方程系统的延迟，最后在其一般设置。 该项目的一个重要组成部分将是数值模拟和数值跟踪分叉周期解。 所有的结果都将被赋予一个适合自然科学的解释。 这个数学项目实现了促进科学知识的计划目标，使保加利亚和美国的领先专家能够联合收割机互补人才，并在共同感兴趣和能力强的领域汇集资源。 ***

9412284 Li This grant supports a US-Bulgaria Joint Cooperative Research Project on "Analytical and Computational Studies of Oscillations in Age-Structured Population Models" between Dr. Jia Li and Dr. Mark J. Friedman of the Department of Mathematical Sciences of the University of Alabama Huntsville, and Dr. Tanya Kostova of the Laboratory of Numerical Methods of the Institute of Mathematics of the Academy of Sciences, Sofia, Bulgaria. The topics of research will include analytical and computational studies of oscillations in age-structured population models. The results of the study are expected to have an impact in both mathematical and biological sciences, as the main goal is to disclose the underlying mechanisms of the possible (and often observed in nature) oscillatory behavior of the size of a single population. Understanding such mechanisms is one of the most important questions in the theory of population dynamics. The collaboration will benefit both sides as the participating researchers have close but different and complementary experience in treating such models. The research will focus on the spectral analysis of the linearization of the age-structured model, which is a nonlinear partial differential-integral equation, on its simplifications in various forms, such as systems of ordinary differential equations and equations with delay, and finally on its general setting. An important part of the project will be numerical simulations and numerical tracing of bifurcating periodic solutions. All results will be given a suitable interpretation for the natural sciences. This project in mathematics fulfills the program objective of advancing scientific knowledge by enabling leading experts in Bulgaria and the United States to combine complementary talents and pool resources in areas of strong mutual interest and competence. ***