Complex system

A complex system is the system composed of many components which may interact with regarded and pointed separately. other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such(a) as energy to direct or setting grid, transportation or communication systems, complex software as alive as electronic systems, social as well as economic organizations like cities, an ecosystem, a living cell, together with ultimately the entire universe.

Complex systems are systems whose behavior is intrinsically unoriented to improvement example due to the dependencies, competitions, relationships, or other nature of interactions between their parts or between a assumption system and its environment. Systems that are "complex" develope distinct properties that occur from these relationships, such(a) as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops, among others. Because such systemsin a wide quality of fields, the commonalities among them realize become the topic of their freelancer area of research. In many cases, it is useful to equal such a system as a network where the nodes live the components and links to their interactions.

The term complex systems often returned to the inspect of complex systems, which is an approach to science that investigates how relationships between a system's parts render rise to its collective behaviors and how the system interacts and forms relationships with its environment. The inspect of complex systems regards collective, or system-wide, behaviors as the essential 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 unit parts and the individual interactions between them.

As an interdisciplinary domain, complex systems draws contributions from many different fields, such(a) as the study of self-organization and critical phenomena from physics, that 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.

Key concepts

Complex systems are chiefly concerned with the behaviors and properties of systems. A system, loosely defined, is a set of entities that, through their interactions, relationships, or dependencies, form a unified whole. this is the always defined in terms of its boundary, which determines the entities that are or are not factor of the system. Entities lying external the system then become part of the system's environment.

A system can exhibit properties that produce behaviors which are distinct from the properties and behaviors of its parts; these system-wide or global properties and behaviors are characteristics of how the system interacts with or appears to its environment, or of how its parts behave say, in response to outside stimuli by virtue of being within the system. The conception of behavior implies that the study of systems is also concerned with processes that take place over time or, in mathematics, some other phase space parameterization. Because of their broad, interdisciplinary applicability, systems opinion play a central role in complex systems.

As a field of study, complex systems is a subset of systems theory. General systems theory focuses similarly on the collective behaviors of interacting entities, but it studies a much broader a collection of matters sharing a common features of systems, including non-complex systems where traditional reductionist approaches may cover viable. Indeed, systems theory seeks to explore and describe all a collection of things sharing a common attribute of systems, and the invention of categories that are useful to researchers across widely varying fields is one of the systems theory's leading objectives.

As it relates to complex systems, systems theory contributes an emphasis on the way relationships and dependencies between a system's parts can develop system-wide properties. It also contributes to the interdisciplinary perspective of the study of complex systems: the notion that divided properties association systems across disciplines, justifying the pursuit of modeling approaches applicable to complex systems wherever they appear. specific concepts important to complex systems, such as emergence, feedback loops, and adaptation, also originate in systems theory.

For a system to exhibit complexity means that the systems' behaviors cannot be easily inferred from its properties. all modeling approach that ignores such difficulties or characterizes them as noise will necessarily produce models that are neither accurate nor useful. As yet no fully general theory of complex systems has emerged for addressing these problems, so researchers must solve them in domain-specific contexts. Researchers in complex systems credit these problems by viewing the chief task of modeling to be capturing, rather than reducing, the complexity of their respective systems of interest.

While no broadly accepted exact definition of complexity exists yet, there are many archetypal examples of complexity. Systems can be complex if, for instance, they have chaotic behavior behavior that exhibits extreme sensitivity to initial conditions, among other properties, or whether they have emergent properties properties that are not apparent from their components in isolation but which written from the relationships and dependencies they form when placed together in a system, or whether they are computationally intractable to improvement example if they depend on a number of parameters that grows too rapidly with respect to the size of the system.

The interacting components of a complex system form a network, which is a collection of discrete objects and relationships between them, usually depicted as a graph of vertices connected by edges. Networks can describe the relationships between individuals within an organization, between logic gates in a circuit, between genes in gene regulatory networks, or between any other set of related entities.

Networks often describe the advice of complexity in complex systems. Studying complex systems as networks, therefore, ensures many useful a formal request to be considered for a position or to be helps to do or have something. of graph theory and network science. Many complex systems, for example, are also complex networks, which have properties such as phase transitions and power-law degree distributions that readily lend themselves to emergent or chaotic behavior. The fact that the number of edges in a complete graph grows quadratically in the number of vertices sheds extra light on the quotation of complexity in large networks: as a network grows, the number of relationships between entities quickly dwarfs the number of entities in the network.

Complex systems often have nonlinear behavior, meaning they mayin different ways to the same input depending on their state or context. In mathematics and physics, nonlinearity describes systems in which a modify in the size of the input does non produce a proportional modify in the size of the output. For a condition change in input, such systems may yield significantly greater than or less than proportional turn in output, or even no output at all, depending on the current state of the system or its argument values.

Of particular interest to complex systems are nonlinear dynamical systems, which are systems of differential equations that have one or more nonlinear terms. Some nonlinear dynamical systems, such as the Lorenz system, can produce a mathematical phenomenon invited as chaos. Chaos, as it applies to complex systems, noted to the sensitive dependence on initial conditions, or "butterfly effect", that a complex system can exhibit. In such a system, small revise to initial conditions can lead to dramatically different outcomes. Chaotic behavior can, therefore, be extremely hard to good example numerically, because small rounding errors at an intermediate stage of computation can cause the model to generate completely inaccurate output. Furthermore, if a complex system returns to a state similar to one it held previously, it may behave totally differently in response to the same stimuli, so chaos also poses challenges for extrapolating from experience.

Another common feature of complex systems is the presence of emergent behaviors and properties: these are traits of a system that are not apparent from its components in isolation but which calculation from the interactions, dependencies, or relationships they form when placed together in a system. Emergence broadly describes the structure of such behaviors and properties, and has a formal request to be considered for a position or to be allowed to do or have something. to systems studied in both the social and physical sciences. While emergence is often used to refer only to the configuration of unplanned organized behavior in a complex system, emergence can also refer to the breakdown of an organization; it describes any phenomena which are unmanageable or even impossible to predict from the smaller entities that make up the system.

One example of a complex system whose emergent properties have been studied extensively is Conway's Game of Life.

When emergence describes the appearance of unplanned order, it is spontaneous order in the social sciences or self-organization in physical sciences. Spontaneous order can be seen in herd behavior, whereby a house of individuals coordinates their actions without centralized planning. Self-organization can be seen in the global symmetry ofcrystals, for instance the apparent radial symmetry of snowflakes, which arises from purely local attractive and repulsive forces both between water molecules and their surrounding environment.

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 increase the stock market, social insect and ant colonies, the biosphere and the ecosystem, the brain and the immune system, the cell and the development embryo, the cities, manufacturing businesses and any human social group-based endeavor in a cultural and social system such as political parties or communities.