Abstract
Complex systems are composed of a large number of individual components. Many of these systems are separable, i.e., they can be split into two coupled subsystems: one with foreground components and another with background components. The former leads to narrow peaks in the frequency spectrum of the system and the latter gives the broad-band part. There is coupling between the two subsystems, but they can be studied separately for purposes of modeling and for analysis of experimental data. Examples from the literature are given from the area of mechanical vibrations, but the approach is quite general and can be adapted to other kinds of problems.
Highlights
Complex systems are composed of a large number of individual components or elements
The conceptual advantage of the separation is that the foreground and background components and subsystems can be studied and understood separately
The foreground components serve as a sink for background energy and in this fashion participate in the process of mechanical vibrations of the entire system
Summary
Complex systems are composed of a large number of individual components or elements. If any measurements are made, the measuring instruments are part of it and contribute to the complexity of the system. The components of the dynamic system may be easy to model, but taken together they give rise to a large number of coupled equations that become virtually intractable This is the main reason why the dynamic behavior of a complex system is often obtained experimentally. The foreground components provide a frequency response that has a small number of sharp, narrow peaks, while the background has a broad-band spectrum. The conceptual advantage of the separation is that the foreground and background components and subsystems can be studied and understood separately They may have completely different physical and mathematical representations.
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