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

9412284 Li本基金支持由美国阿拉巴马大学亨茨维尔分校数学科学系的Jia Li博士、Mark J. Friedman博士和保加利亚索非亚科学院数学研究所数值方法实验室的Tanya Kostova博士共同开展的“年龄结构人口模型振荡的分析与计算研究”的美国-保加利亚联合合作研究项目。研究主题将包括年龄结构人口模型振荡的分析和计算研究。该研究的结果预计将对数学和生物科学产生影响，因为其主要目标是揭示单个种群规模可能（并且在自然界中经常观察到）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。此次合作将使双方受益，因为参与研究的研究人员在处理这些模型方面有着接近但不同且互补的经验。研究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，研究其各种形式的简化，如常微分方程组和时滞方程，最后研究它的一般设置。该项目的一个重要部分将是分岔周期解的数值模拟和数值跟踪。所有的结果都将被给予自然科学的适当解释。这个数学项目实现了推进科学知识的计划目标，使保加利亚和美国的顶尖专家能够在共同感兴趣和有能力的领域结合互补的人才和汇集资源。＊＊＊

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. ***