General systems analysis

The analysis of complex systems is a constituent part of nearly every sci- entic discipline. Astronomy, for example, deals with the largest systems in time and space, with cosmic objects like galaxies, stars, and the forces that act between them, such as gravitation. Biology is engaged with living beings and their mutual relations, e.g., predator-prey systems. Interactions between human individuals and social groups form the research topics of the social sciences, and interactions of organs of an individual are part of the medical sciences.

Since the middle of the 20th century, the reductionist approach, i.e., the bottom-up explanation of the whole from the properties of its elements, has been challenged by the perception that complex phenomena often re- sult from (rather simple) non-linear interactions between the elements or subsystems. Moreover, the rules that determine the systems' behaviors have turned out to be similar in seemingly different systems. As a result, interdisciplinary research fields such as the general systems science and cybernetics emerged. Systems analysis and computer science (informatics) are late-comers in that historical chain of events.

The most important topics of systems analysis are data analysis, modeling, simulation, and synthesis relying on optimization.

The analysis of a system starts with its observation, which supplies var- ious data. Selecting and processing these recorded measurements by us- ing mathematical and statistical methods is usually known as data analy- sis. The methods of descriptive statistics provide fundamental information about the system, whereas the techniques of conclusive statistics give us knowledge concerning the statistical relevance of the measured data. Data analysis precedes the other phases of systems analysis and in the attainable results to a large extent.

Mostly, the investigation of a system cannot be solely based on real-world experimentation because it is too expensive, too risky or even impossible at all. In this case, computer models can often be utilized as substitutes of reality. In order to do so, the model has to mimic the behavior of the original system closely enough depending on the aim of the investigation. With regard to the information available and the given problem we can choose a purely descriptive, an explaining, a normative, or a mixed model. In addition to analytical models the more powerful computer models are used more and more often. Only these combine a great flexibility with a high processing speed and make it possible to comprehend a complex system.

Simulation studies based on computer models generated in the modeling phase can help to get insight into the behavior of a given system even in the case of complex systems with dierent restrictions. Thus, computer simu- lation is nowadays well established as a fundamental approach to analysis.

Frequently, if a mathematical or computer model is given, the goal of systems analysis is to find a set of parameters that yields a desired system behavior. Often, analytical methods fail because the model is not given in a closed analytical form. Trying all possible scenarios leads to a best solution only for a very small set of alternatives. That is why algorithms locating the global or at least one good local optimum with a high probability but using only reasonable computing resources become more and more important. In this connection, knowledge in the area of nonlinear dynamics is needed to handle the often observed chaotic behavior of a system for a specic parameter range. More often than not one has to deal with several contradictory objectives.