"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 the entire universe."
This subfield studies how systems composed of many interacting components can create complex and often unpredictable behaviors.
Systems theory: The study of complex systems, including the components, processes, and interactions within them.
Nonlinear dynamics: The study of systems that are sensitive to initial conditions and exhibit behaviors such as chaos, bifurcation, and self-organization.
Agent-based modeling: A simulation approach that models the behavior of individual agents to understand emergent system-level behaviors.
Fractal geometry: The study of geometric patterns that repeat at different scales, and are commonly found in natural systems.
Network analysis: The study of the structure, properties, and dynamics of networks, including their formation and evolution.
Game theory: The study of decision-making in complex, interdependent systems, including the strategies and outcomes of games played in such systems.
Information theory: The study of information, entropy, and communication in complex systems.
Artificial life: The study of life-like systems, often modeled through computer simulations, that exhibit characteristics such as self-replication, adaptation, and evolution.
Complexity metrics: Quantitative measures used to describe and characterize the complexity of systems, including entropy, fractal dimension, and network properties.
Chaos theory: The study of deterministic systems that exhibit sensitive dependence on initial conditions and unpredictable, nonlinear behavior.
Emergence: The study of how new properties, structures, or behaviors can arise from the interactions of simpler components in complex systems.
Adaptive systems: The study of systems capable of adapting to changing environments, including biological, social, and technological systems.
Self-organization: The study of how ordered patterns can arise spontaneously from the interactions of many simple components in complex systems.
Information processing: The study of how information is processed, stored, and transmitted in complex systems, including the relationship between information and complexity.
Evolutionary dynamics: The study of how complex systems can evolve over time, including the role of genetic and cultural evolution in shaping biological and social systems.
Chaos Theory: This theory studies the behavior of dynamic systems that are highly sensitive to initial conditions. It deals with the prediction and control of random, unpredictable phenomena.
Fractal Theory: Fractal theory deals with repetitive patterns that occur at different scales in natural processes. It is concerned with the study of self-similarity and self-organization in complex systems.
Network Theory: Network theory deals with complex systems composed of interconnected entities, which gives rise to emergent phenomena. It examines the properties of networks and how they influence the behavior of the systems they represent.
Information Theory: Information theory deals with the complexity of information processing, storage, and transmission. It describes how information is encoded, decoded, and transmitted, and how it can be compressed to reduce complexity.
Game Theory: Game theory deals with the strategic interactions between individuals or groups of individuals. It assumes that people behave rationally and predictably, and that interactions can be analyzed mathematically.
Systems Theory: Systems theory deals with the study of complex systems that exhibit emergent behavior. It focuses on the relationships between the components of the system and how they give rise to the behavior of the system as a whole.
Evolutionary Theory: Evolutionary theory deals with the study of the evolution of complex systems over time. It examines how genetic, environmental, and social factors influence the development of complex systems, and how they adapt to changing circumstances.
Complexity Science: Complexity science is an interdisciplinary field that combines elements of chaos theory, network theory, systems theory, and other disciplines to study complex systems. It examines the behavior of complex systems, and how they arise from simple rules and interactions.
"Systems that are 'complex' have distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops, among others."
"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 study of complex systems regards collective, or system-wide, behaviors as the fundamental object of study."
"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."
"Complex systems draws contributions from many different fields, such 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."
"How the system interacts and forms relationships with its environment."
"Distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops."
"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."
"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."
"Distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops."
"The study of complex systems investigates how relationships between a system's parts give rise to its collective behaviors."
"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)."
"Distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops."
"Complex systems draw contributions from many different fields, such as the study of self-organization and critical phenomena from physics."
"Distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops."
"Statistical physics, information theory, nonlinear dynamics, anthropology, computer science, meteorology, sociology, economics, psychology, and biology."
"How the system interacts and forms relationships with its environment."
"Distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops."
"Examples of complex systems are Earth's global climate, organisms, the human brain, an ecosystem, a living cell, and ultimately the entire universe."