A complex system can be roughly defined as a system made up of a large number of interacting elements. This interaction creates collective structures on many levels. Typical examples are found in nature, from bio-molecules and living cells to human social systems and to the ecosphere, or in sophisticated artificial systems such as internet or large scale, distributed software systems .
The specifics of a complex system, in general hardly considered by traditional science, lie in the formation of a far from banal super structure that often determines the behavior of the system and can be found in the individual properties of the single parts.
Not only the emergent properties in complex systems derive from the interactions at lower levels amongst the parts, but also the global characteristics that are created, influence the lowest levels in a feedback mechanism. It is often the case that a complex system presents extraordinary properties of robustness against disturbances even on a vast scale.
These systems have an inherent capacity to adapt and maintain their stability. Since complexity requires an analysis on largely different spatial and temporal scales, scientists face the double challenge of describing the behavior of complex systems in an efficient way, as well as developing methods for their control.
Complex systems require an interdisciplinary approach. In fact, the universal questions that they present can be formulated in an analogous way in a wide spectrum of disciplines from biology and computer networks to our society. The standard methods of the respective specialized disciplines rarely take into account the multi-level approach that is necessary in the context of complex systems and that can only be achieved with an integrated and multi-disciplinary approach.
The questions before us are many. An important aspect to take into consideration are the different levels of organization. In complex systems individual interactions cause the emergence of a behavior and a collective organization. This leads to important questions: i) what are the various levels of organization and their characteristic scales in space and time? ii) how do the reciprocal influences between individual and collective behaviors work? iii) how can we simultaneously study the various levels of organization as often required in problems in biology and social sciences? iv) how can we characterize emerging structures in an efficient way?
In the current context of globalization and of increasing importance of the far reaching interactions between the various networks, the analysis of complex systems helps to explore many different questions relating to economic development, social cohesion or the environment on different geographic scales. Finally, the rapidly growing influence of computer and communications technology, and the great number of decentralized networks that depend on this new technology, absolutely require research in complex systems and the solutions that emerge from it. In particular, the current trend from processors to networks causes the emergence of the so-called diffuse intelligence, which plays a growing role on how the future networks will be designed and managed.