Center for Complex Systems Research

« The Paradigm of Complex Systems »

Stephen Hawking : "I think the next century will be the century of complexity."

Complex system is a new field of science studding how parts give rise to the collective behaviors of the system and how interacts with its environment.

The study of complex system is about understanding the indirect effect. Problems can be difficult to solve and hard to understand because of causes and effects are not obviously related. Pushing a complex system ‘‘here’’ can often has effects “over there” because the parts are interdependent. Complexity is usually greatest in systems whose component are arranged in some intricate difficult to understand pattern. In the case of a dynamical systems when the outcome of some process is difficult to predict from its initial state. There are three interrelated approaches to modern study of complex system: 1) how interactions give rise to pattern of behavior 2) understanding the ways of describing complex systems and 3) the process of formation of complex systems through pattern formation and evolution.    

Dynamical complex systems have dissipative structure i.e. organized state of a physical system whose integrity is maintained while it is far from equilibrium. Dissipative dynamical systems are caricaturized by some sort of internal friction that tends to contract   space volume elements. Phase space contraction in turn allows approaching a subset of the phase space called an attractor (consisting a fixed point, a periodic cycle, strange attractor) that time goes to infinity.

Self-organization and chaotic behavior is usually the main feature of dynamical complex systems. Deterministic chaos refers to irregular motion generated by nonlinear systems involving according to dynamical lows that uniquely determine the state of the system at all times from knowledge of the system previous history.