U.S.-Chile Planning Visit: Some Aspects of the Qualitative Theory of Functional Differential Equations

9910809Ivanov这一美洲计划奖将支持宾夕法尼亚州立大学的A.F.Ivanov博士前往智利，计划一个研究项目，旨在定性和数值研究时滞微分方程组和此类方程组的解的全球动力学，包括周期解的存在性、稳定性、对参数的依赖性和分叉、混沌行为以及平衡点的全局稳定性。合作者将是智利大学的曼努埃尔·平托博士和谢尔盖·特罗菲姆丘克。该小组还包括博士后助理和研究生。该项目有可能解决几个重要的理论问题，从而进一步发展该领域的定性理论，以及将理论问题的发展与实际应用中的问题联系起来的能力。为了实现该项目的目标，研究人员将使用现代动力系统理论、非线性分析、常微分方程组和时滞微分方程的定性理论、计算数学和摄动方法的各种技术和方法。

9910809IvanovThis Americas Program award will support Dr. A. F. Ivanov, Pennsylvania State University, to travel to Chile, to plan a research project aimed at the study, both qualitative and numerical, of the global dynamics of solutions of delay differential equations and systems of such equations including questions of the existence, stability, dependence on parameters and bifurcations of periodic solutions, chaotic behavior, and global stability of equilibria. Collaborators will be Dr. Manuel Pinto and Sergei Trofimchuk, Universidad de Chile. The group also includes postdoctoral associates and graduate students.The project has the potential to solve several important theoretical problems, thus further developing the qualitative theory of the field, as well as the ability to bridge the development of theoretical issues with problems coming from actual applications. To achieve the goals of the project, the researchers will use various techniques and methods from the modern theory of dynamical systems, nonlinear analysis, qualitative theory of ordinary and delay differential equations, computational mathematics and perturbation methods.