Complex system

Collective intelligenceCollective actionSelf-organized criticalityHerd mentalityPhase transitionAgent-based modellingSynchronizationAnt colony optimizationParticle swarm optimizationSocial network analysisSmall-world networksCommunity identificationCentralityMotifsGraph TheoryScalingRobustnessSystems biologyDynamic networksEvolutionary computationGenetic algorithmsGenetic programmingArtificial lifeMachine learningEvolutionary developmental biologyArtificial intelligenceEvolutionary roboticsReaction-diffusion systemsPartial differential equationsDissipative structuresPercolationCellular automataSpatial ecologySelf-replicationSpatial evolutionary biologyOperationalizationFeedbackSelf-referenceGoal-orientedSystem dynamicsSensemakingEntropyCyberneticsAutopoiesisInformation theoryComputation theoryOrdinary differential equationsIterative mapsPhase spaceAttractorsStability analysisPopulation dynamicsChaosMultistabilityBifurcationRational choice theoryBounded rationalityIrrational behaviourA complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, social and economic organizations (like cities), an ecosystem, a living cell, and ultimately the entire universe. A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, social and economic organizations (like cities), an ecosystem, a living cell, and ultimately the entire universe. 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. 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 own 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 the links 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 draws contributions from many different fields, such as the study of self-organization 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. Complex systems is chiefly concerned with the behaviors and properties of systems. A system, broadly defined, is a set of entities that, through their interactions, relationships, or dependencies, form a unified whole. It is always defined in terms of its boundary, which determines the entities that are or are not part of the system. Entities lying outside 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 external stimuli) by virtue of being within the system. The notion 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 concepts 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 class of systems, including non-complex systems where traditional reductionist approaches may remain viable. Indeed, systems theory seeks to explore and describe all classes of systems, and the invention of categories that are useful to researchers across widely varying fields is one of systems theory's main objectives.