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

Ivanov0203702这一美国-智利项目奖将支持宾夕法尼亚州立大学的A.F.Ivanov博士与圣地亚哥智利大学的Manuel A.Pinto博士和Sergei I.Trofimchuk博士以及智利概念生物大学的Samuel A.Castillo博士之间的合作研究。这个项目的目的是定性和数值地研究泛函微分方程解的全局动力学，包括周期解的存在性、稳定性、参数依赖性和分叉、混沌行为和平衡点的全局稳定性。它将着重研究方程的全局稳定性和周期解，模拟现实生活中的现象，以及差分式和离散化泛函微分方程的渐近行为。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.