Complicated Dynamics and Their Implications for System Design Methodologies

这项研究的目的是解释、适应和扩展与某些局部和非局部分叉相关的概念和技术，使它们成为系统设计、稳定性和反馈控制机制的有价值的工具。特别是，它将集中在理论问题，对几个工程系统的适用性，以及计算机辅助图形和计算。关于局部分叉、混沌和Arnold扩散的最新结果将被应用并进一步发展。局部分叉、混沌和Arnold扩散构成了一种不受欢迎的不稳定形式，在当前的工程设计和控制方法中必须系统地解决这一问题。特别是，它们在电力系统、约瑟夫森结或自适应和反馈控制系统中是不可取的。这项工作的结果可以作为广泛的工程系统的适当设计准则。

The objective of this research is to interpret, adapt and extend the concepts and techniques associated with certain local and nonlocal bifurcations so that they become valuable tools for system design, stability and feedback control mechanisms. In particular, it will focus on theoretical issues, applicability to several engineering systems, and computer-assisted graphics and computations. Recent results on local bifurcations, chaos and Arnold diffusion will be employed and further developed. Local bifurcations, chaos and Arnold diffusion constitute an undesirable form of instability which has to be systematically addressed in current engineering design and control methodologies. In particular, they are not desirable in power systems, Josephson junctions or adaptive and feedback control systems. The results of this work could be used as proper design criteria for wide class of engineering systems.