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. ***
