Complex Systems

Motto:

For more then thirty years, scientist are studing complex systems appearing in a vast number of natural phenomena which are observed in the whole spectrum of scientific fields such as bilogy, medicine, social sciences, physics, mathematics, computer science and many others. Surprisingly, and despide diversity of those fields, there are some common features observed within complex systems. They are typically composed of vast number of simple and locally operating parts which are mutually inteacting and producing global complex responses. Self-organization and emergence are are often observed in complex systems. Evolution is typically driven by dissipation of energy or information.

-- J. Kroc, 2006

Why complex systems?

During evolution of natural sciences a critical knowledge point had been achieved in numerous research fields simultaneously. At this moment scientists realized that classical approaches are not longer useful to formulate a wide range of problems such as -- for example -- brain, ecology, sociology, pedestrian, and human immune cells behaviour. Critical difficulties in the formulation and solution of these problems are usually faced when classical methods are used to solve them. The most promising theory that enables us to overcome such difficulties is the theory of Complex Systems. Complex Systems provide a completely new paradigm of formulation and solution of scientific problems.

Nature "works" with complex systems -- or use them -- at least for hundreds of millions years if not from the very beginning of the Universe. Simply said, the Life is based on this concept. On one hand, some examples are ant-colony, birds flocking, fish schools, ecosystem, and sociology behaviour on the macroscopic level. On the other hand, a living cell itself and immune system are operating on the microscopic level. As an example, the general idea of the formulation/creation of a complex system is explained on the ant colony behaviour in the following text.

Simple example - Ant Colony Behaviour

An ant colony is created from many identical copies of one entity named an ant. One ant is simply nothing but once we put together hundreds of ants -- or more -- then a "strange" behaviour appears. Such behaviour finally leads to the creation of a regular ant colony. One can think about a miracle or so, but the truth lies somewhere else. We have to realize that there is NO any ANT LEADER that "owns" building plans and "tells" the others what to do. Nothing like this is true. Every particular ant has just a restricted instruction list -- encoded reactions on stimuli -- and simply follows them.

A quite surprising message of this "example" is the simple fact that every particular ant response on a restricted list of actions -- number of reactions layes somewhere between 20 and 40 --, the exact number depends on the ant species. We know that ants are able to -- and they do so -- build the ant-colony, collect food, defend colony, attack another colony, grow new ants up and other things, all with no more than 40 instructions. It was and still is a big surprise for scientific community. Naturally, such behaviour leads to ...

Definition of Complex Systems

"Complex systems" appear through interactions and non-linear dependencies in systems of many objects. Surprisingly, it is found in many cases that those interactions and non-linear dependencies have quite simple nature. The field includes many research areas that are quite diverse, such as

cellular automata, artificial life, chaos, criticality, evolutionary computation, neural networks, genetic algorithms, parallel computing, physics, biology, economy, medicine, sociology and many others areas.

Definition of Complex Systems in one simple sentence reads:

The whole is more than a mere sum of its parts.

Recommended Introductory Books

Advanced Books: