U.S.-Chile Program: Aspects of the Qualitative Theory of Functional Differential Equations

这项美国-智利项目将为宾夕法尼亚州立大学的A. F. Ivanov博士和哥伦比亚大学的A. F. Ivanov博士之间的合作研究提供支持。圣地亚哥智利大学的Manuel A. Pinto和Sergei I. Trofimchuk，以及智利concepte Bio-Bio大学的Samuel A. Castillo博士。他们将研究泛函微分方程的定性理论。本项目旨在定性和数值研究泛函微分方程解的整体动力学问题，包括周期解的存在性、稳定性、参数依赖性和分岔性、混沌行为和平衡点的整体稳定性问题。它将着重研究差分和离散泛函微分方程的全局稳定性和周期解，这些方程模拟了现实生活中的现象和渐近行为。该项目的意义在于它有可能解决几个重要的理论数学问题，从而进一步发展该领域的定性理论。

Ivanov0203702This U.S.-Chile Program award will provide support for cooperative research between Dr. A. F. Ivanov of Pennsylvania State University and Drs. Manuel A. Pinto and Sergei I. Trofimchuk of the Universidad de Chile in Santiago, and Dr. Samuel A. Castillo of Universidad del Bio-Bio in Conception, Chile. They will work on aspects of the qualitative theory of functional differential equations.The aim of this project is to study both qualitatively and numerically, the global dynamics of solutions of functional differential equations and systems of such equations including questions of the existence, stability, dependence on parameters and bifurcation of periodic solutions, chaotic behavior, and global stability of equilibria. It will emphasize the study of global stability and periodic solutions of equations modeling real life of phenomena and asymptotic behavior in difference and discretized functional differential equations. The significance of the project lies in its potential to solve several important theoretical mathematical problems, thus further developing the qualitative theory of the field.