Complicated Dynamics and Their Implications for System Design Methodologies

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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.