Complex systems Complex systems present problems both in mathematical modelling and philosophical foundations. The study of complex systems represents a new approach to science that investigates how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment.[1] Such systems are used to model processes in computer science, biology,[2] economics, physics, chemistry,[3] and many other fields. The key problems of complex systems are difficulties with their formal modelling and simulation. For systems that are less usefully represented with equations various other kinds of narratives and methods for identifying, exploring, designing and interacting with complex systems are used. Overview[edit] History[edit] A history of complexity science Typical areas of study[edit] Complexity management[edit] Complexity economics[edit] Complexity and modeling[edit] Complexity and chaos theory[edit] 1. Institutes and research centers[edit]
Complexity There is no absolute definition of what complexity means, the only consensus among researchers is that there is no agreement about the specific definition of complexity. However, a characterization of what is complex is possible.[1] Complexity is generally used to characterize something with many parts where those parts interact with each other in multiple ways. The study of these complex linkages is the main goal of complex systems theory. In science,[2] there are at this time a number of approaches to characterizing complexity, many of which are reflected in this article. Overview[edit] Definitions of complexity often depend on the concept of a "system"—a set of parts or elements that have relationships among them differentiated from relationships with other elements outside the relational regime. Some definitions relate to the algorithmic basis for the expression of a complex phenomenon or model or mathematical expression, as later set out herein. Varied meanings of complexity[edit]
Systemtheorie Die Systemtheorie ist sowohl eine allgemeine und eigenständige Disziplin als auch ein weitverzweigter und heterogener Rahmen für einen interdisziplinären Diskurs, der den Begriff System als Grundkonzept führt. Es gibt folglich sowohl eine allgemeine „Systemtheorie“ als auch eine Vielzahl unterschiedlicher, zum Teil widersprüchlicher und konkurrierender Systemdefinitionen und -begriffe. Es hat sich heute jedoch eine relativ stabile Reihe an Begriffen und Theoremen herausgebildet, auf die sich der systemtheoretische Diskurs bezieht. Geschichte[Bearbeiten] Der Begriff Allgemeine Systemtheorie geht auf den Biologen Ludwig von Bertalanffy zurück. Kulturgeschichtlich geht der Systembegriff bis auf Johann Heinrich Lambert zurück und wurde unter anderem von Johann Gottfried Herder übernommen und ausgearbeitet. Die moderne Systemtheorie beruht auf unabhängig voneinander entwickelten Ansätzen, die später synthetisiert und erweitert wurden: Der Begriff Systemtheorie bzw. Kybernetik[Bearbeiten]
Complexity theory and organizations Application of complexity theory to strategy Complexity theory and organizations, also called complexity strategy or complex adaptive organizations, is the use of the study of complexity systems in the field of strategic management and organizational studies.[1][2][3][4] It draws from research in the natural sciences that examines uncertainty and non-linearity.[5] Complexity theory emphasizes interactions and the accompanying feedback loops that constantly change systems. While it proposes that systems are unpredictable, they are also constrained by order-generating rules.[6]: 74 Complexity theory has been used in the fields of strategic management and organizational studies. Complex adaptive systems [edit] Organizations can be treated as complex adaptive systems (CAS) as they exhibit fundamental CAS principles like self-organization, complexity, emergence,[9] interdependence, space of possibilities, co-evolution,[10][11][12] chaos,[13][14][11][12] and self-similarity.[7][15][11][12]
Complex adaptive system They are complex in that they are dynamic networks of interactions, and their relationships are not aggregations of the individual static entities. They are adaptive in that the individual and collective behavior mutate and self-organize corresponding to the change-initiating micro-event or collection of events.[1][2] Overview[edit] The term complex adaptive systems, or complexity science, is often used to describe the loosely organized academic field that has grown up around the study of such systems. The fields of CAS and artificial life are closely related. The study of CAS focuses on complex, emergent and macroscopic properties of the system.[3][11][12] John H. General properties[edit] What distinguishes a CAS from a pure multi-agent system (MAS) is the focus on top-level properties and features like self-similarity, complexity, emergence and self-organization. Characteristics[edit] Some of the most important characteristics of complex systems are:[14] Robert Axelrod & Michael D.
Computational sociology Branch of the discipline of sociology Computational sociology is a branch of sociology that uses computationally intensive methods to analyze and model social phenomena. Using computer simulations, artificial intelligence, complex statistical methods, and analytic approaches like social network analysis, computational sociology develops and tests theories of complex social processes through bottom-up modeling of social interactions.[1] In relevant literature, computational sociology is often related to the study of social complexity.[5] Social complexity concepts such as complex systems, non-linear interconnection among macro and micro process, and emergence, have entered the vocabulary of computational sociology.[6] A practical and well-known example is the construction of a computational model in the form of an "artificial society", by which researchers can analyze the structure of a social system.[2][7] History[edit] Background[edit] Systems theory and structural functionalism[edit]
Cellular automaton The concept was originally discovered in the 1940s by Stanislaw Ulam and John von Neumann while they were contemporaries at Los Alamos National Laboratory. While studied by some throughout the 1950s and 1960s, it was not until the 1970s and Conway's Game of Life, a two-dimensional cellular automaton, that interest in the subject expanded beyond academia. In the 1980s, Stephen Wolfram engaged in a systematic study of one-dimensional cellular automata, or what he calls elementary cellular automata; his research assistant Matthew Cook showed that one of these rules is Turing-complete. Wolfram published A New Kind of Science in 2002, claiming that cellular automata have applications in many fields of science. The primary classifications of cellular automata as outlined by Wolfram are numbered one to four. Overview[edit] The red cells are the von Neumann neighborhood for the blue cell, while the extended neighborhood includes the pink cells as well. A torus, a toroidal shape History[edit]
Complex systems biology Complex systems biology (CSB) is a branch or subfield of mathematical and theoretical biology concerned with complexity of both structure and function in biological organisms, as well as the emergence and evolution of organisms and species, with emphasis being placed on the complex interactions of, and within, bionetworks,[1] and on the fundamental relations and relational patterns that are essential to life.[2][3][4][5][6] CSB is thus a field of theoretical sciences aimed at discovering and modeling the relational patterns essential to life that has only a partial overlap with complex systems theory,[7] and also with the systems approach to biology called systems biology; this is because the latter is restricted primarily to simplified models of biological organization and organisms, as well as to only a general consideration of philosophical or semantic questions related to complexity in biology. Network Representation of a Complex Adaptive System Telomerase structure and function
Self-organization Self-organization occurs in a variety of physical, chemical, biological, robotic, social and cognitive systems. Common examples include crystallization, the emergence of convection patterns in a liquid heated from below, chemical oscillators, swarming in groups of animals, and the way neural networks learn to recognize complex patterns. Overview[edit] The most robust and unambiguous examples[1] of self-organizing systems are from the physics of non-equilibrium processes. Self-organization is also relevant in chemistry, where it has often been taken as being synonymous with self-assembly. Self-organization usually relies on three basic ingredients:[3] Strong dynamical non-linearity, often though not necessarily involving positive and negative feedbackBalance of exploitation and explorationMultiple interactions Principles of self-organization[edit] History of the idea[edit] Sadi Carnot and Rudolf Clausius discovered the Second Law of Thermodynamics in the 19th century. Developing views[edit]
Complex response A complex response refers to an environmental reaction to change that occurs at multiple levels to multiple objects, and can induce a chain reaction of responses to a single initial change. It is akin to the butterfly effect: one small event (change) can cascade through a given system creating new agents of change, and operating at several levels. The term is most commonly used in fluvial geomorphology, or the study of river systems and changes within those systems.[1] complex system