Complex systems present problems in mathematical modelling. Complex systems is a new approach to science that studies how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment.
The equations from which complex system models are developed generally derive from statistical physics, information theory and non-linear dynamics, and represent organized but unpredictable behaviors of systems of nature that are considered fundamentally complex. The physical manifestations of such systems cannot be defined, so the usual choice is to refer to "the system" as the mathematical information model, without referring to the undefined physical subject the model represents. One of a variety of journals using this approach to complexity is Complex Systems.
Such systems are used to model processes in computer science, biology,economics, physics, chemistry, and many other fields. It is also called complex systems theory, complexity science, study of complex systems, sciences of complexity, non-equilibrium physics, and historical physics. A variety of abstract theoretical complex systems is studied as a field of mathematics.