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A complex system is a system composed of many components which may interact with each other.[1] Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and, ultimately, for some authors, the entire universe.[2][3][4]
Complex systems are systems whose behavior is intrinsically difficult to model due to the dependencies, competitions, relationships, or other types of interactions between their parts or between a given system and its environment.[5] Systems that are "complex" have distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops, among others.[6] Because such systems appear in a wide variety of fields, the commonalities among them have become the topic of their independent area of research. In many cases, it is useful to represent such a system as a network where the nodes represent the components and links to their interactions.
The term complex systems often refers to the study of complex systems, which is an approach to science that investigates how relationships between a system's parts give rise to its collective behaviors and how the system interacts and forms relationships with its environment.[7] The study of complex systems regards collective, or system-wide, behaviors as the fundamental object of study; for this reason, complex systems can be understood as an alternative paradigm to reductionism, which attempts to explain systems in terms of their constituent parts and the individual interactions between them.
As an interdisciplinary domain, complex systems draw contributions from many different fields, such as the study of self-organization and critical phenomena from physics, of spontaneous order from the social sciences, chaos from mathematics, adaptation from biology, and many others. Complex systems is therefore often used as a broad term encompassing a research approach to problems in many diverse disciplines, including statistical physics, information theory, nonlinear dynamics, anthropology, computer science, meteorology, sociology, economics, psychology, and biology.
[S]pecial issue of Science on 'Complex Systems' featuring many key figures in the field (Science 2 April 1999) [...] [:] 6. 'A complex system is literally one in which there are multiple interactions between many different components.' (40, p. 105)
The following quotations (apart from the last one) come from a special issue of Science on 'Complex Systems' featuring many key figures in the field (Science 2 April 1999) [:] 8. 'In recent years the scientific community has coined the rubric 'complex system' to describe phenomena, structure, aggregates, organisms, or problems that share some common theme: (i) They are inherently complicated or intricate ...; (ii) they are rarely completely deterministic; (iii) mathematical models of the system are usually complex and involve non-linear, ill-posed, or chaotic behavior; (iv) the systems are predisposed to unexpected outcomes (so-called emergent behaviour).' (14, p. 410)
The following quotations (apart from the last one) come from a special issue of Science on 'Complex Systems' featuring many key figures in the field (Science 2 April 1999) [...] [:] 3. 'In a general sense, the adjective 'complex' describes a system or component that by design or function or both is difficult to understand and verify. ...complexity is determined by such factors as the number of components and the intricacy of the interfaces between them, the number and intricacy of conditional branches, the degree of nesting, and the types of data structures.'(50, p. 92)
The following quotations (apart from the last one) come from a special issue of Science on 'Complex Systems' featuring many key figures in the field (Science 2 April 1999) [...] [:] 4. 'Complexity theory indicates that large populations of units can self-organize into aggregations that generate pattern, store information, and engage in collective decision-making.' (39, p. 99)