The term system derives from the Greek term \(\sigma\upsilon\sigma\tau\varepsilon\mu\alpha\) meaning "being put together". It is an analytical term, implying that systems do not "exist" in the sense of physical objects. In a certain sense, the term could be regarded as artificially made up to generate order with its use (although this can be said of pretty much every term).
Since order is relative, it should be emphasized that systems do not exist independently of an observer. It is the observer of a system, who uses the term in order to indicate something which to him seems put together. Usually he does this by distinguishing this something from other things or phenomena which seem not, or not so orderly put together. To the observer these other things or phenomena are the environment of the system. Systems are always relative to their environments. As there is no system without an observer, there is also no system without an environment.
To the observer, the environment, in seeming less orderly or less being put together, is more complex than the system. To denote something as a system hence is a form of complexity reduction or, what is the same, a form of order generation. A system hence is a sphere, artificially (and temporarily) defined by an observer, in which, in the eyes of this observer, complexity is reduced in respect to the environment of this sphere. To give an example: I might define the items on my writing table as a system in regard to the (more complex or more disordered) other things in my room. This however, might seem completely different to any other observer, who does not gain an advantage from calling the items on my writing table a system.
However, if observers themselves are "being put together", for example as scientists in a science system, they might have common (since interconnected) ways of observing. Therefore, they might use the term system in a similar scientific-analytical way. They do this to bring order to an otherwise unordered (i.e. complex) set of components. Scientists most commonly call something a system if three features can be discerned:
Since systems imply order, they refer to something that in a certain way seems more than the sum of its parts. The parts by themselves might seem loose and unordered. To organize them into a system by finding or defining reasonable ways of how these parts interconnect or interact, adds something to the formerly unordered mess. Thereby the whole becomes more than the sum of its parts. In this respect, systems scientists speak of the emergence of a system.
Emergence indicates that a system as a whole might have qualities or dynamics that its components on their own miss. A widely discussed example of this somehow surprising property is water. Water consists of oxygen and hydrogen, both of which are highly inflammable. Being put together however, these components interact and create water which extinguishes fire. Another simple example of an emergent system with eigenbehavior is the traffic jam, consisting of a multitude of individuals whose aim it is to get to their destination as fast as possible. In interaction however, they might cause the opposite.
More formally and abstractly, the emergent eigenbehavior of systems can be demonstrated and studied on the example of Cellular automata. Additionally it will be discussed in the sections on attractors, agent-based modeling and game theory.
Systems hence behave in a particular way which might differ from, or even contradict the way their components behave. Systems follow their own particular logics, their eigenlogics. This is the reason to conduct systems sciences as a distinct scientific discipline.
Analytically, one might distinguish simpler systems, which consist of rather small sets of interacting components and usually can be analyzed with the help of equation-based methods (EBM), from complex systems, usually consisting of considerable more components that interact in a way which cannot reasonably be modeled with mathematical means. Complex systems therefore often are analyzed by ways of computer simulations. It should be emphasized however, that what is simple and what is complex in this regard again depends on the observer. The delimitation is not absolute, and simple systems too can show quite irritating complex behavior. Nevertheless, to give orientating examples for the one and the other: a typical predator-prey-system as consisting of two or three interacting species could be seen as a rather simple system that can be modeled with equation-based methods; a diffusion system in which individual contacts matter could be seen as a rather complex system that defies modeling with equation-based means. This system rather would be analyzed by way of agent-based modeling (ABM). The difference between equation-based (EBM) and agent-based methods (ABM) is discussed here.