Complex system

A complex system is a system composed of many components that interact with one another. 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.

The behavior of a complex system is intrinsically difficult to model due to the dependencies, competitions, relationships, and other types of interactions between their parts or between a given system and its environment. Systems that are "complex" have distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops, among others. 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 represent 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. 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.

Complex systems can be:

Complex adaptive systems are special cases of complex systems that are adaptive in that they have the capacity to change and learn from experience. Examples of complex adaptive systems include the international trade markets, social insect and ant colonies, the biosphere and the ecosystem, the brain and the immune system, the cell and the developing embryo, cities, manufacturing businesses and any human social group-based endeavor in a cultural and social system such as political parties or communities.

A system is decomposable if the parts of the system (subsystems) are independent from each other, for example the model of a perfect gas consider the relations among molecules negligible.

In a nearly decomposable system, the interactions between subsystems are weak but not negligible, this is often the case in social systems. Conceptually, a system is nearly decomposable if the variables composing it can be separated into classes and subclasses, if these variables are independent for many functions but affect each other, and if the whole system is greater than the parts.