Complexity science

Complex systems present problems both in mathematical modelling and philosophical foundations. The study of complex systems is an approach to science that investigates 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 subject is also sometimes called complex systems theory, complexity science, study of complex systems, complex networks, network science, and sciences of complexity.

The equations from which models of complex systems are developed generally derive from statistical physics, information theory, and non-linear dynamics and represent organized but unpredictable behaviors of natural systems that are considered fundamentally complex. Often times, the physical manifestations of such systems are difficult to define, and so it is common to identify "the system" with the mathematical model rather than referring to the undefined physical subject the model represents. Such a systems approach is often used in computer science, biology,economics, physics, chemistry, architecture, and many other fields. A variety of abstract theoretical complex systems is studied as a field of mathematics.

The key problems of complex systems are difficulties with their formal modelling and simulation. From such a perspective, in different research contexts complex systems are defined on the basis of their different attributes. Since all complex systems have many interconnected components, the science of networks and network theory are important and useful tools for the study of complex systems. A theory for the resilience of system of systems represented by a network of interdependent networks was developed by Buldyrev et al. A consensus regarding a single universal definition of complex system does not yet exist.

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