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. It is also called complex systems theory, complexity science, study of complex systems, sciences of complexity, non-equilibrium physics, and historical physics. 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 1. Americas Europe
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
Cascading failure An animation demonstrating how a single failure may result in other failures throughout a network. A cascading failure is a failure in a system of interconnected parts in which the failure of a part can trigger the failure of successive parts. Such a failure may happen in many types of systems, including power transmission, computer networking, finance and bridges. Cascading failures usually begin when one part of the system fails. When this happens, nearby nodes must then take up the slack for the failed component. Cascading failure in power transmission[edit] Cascading failure is common in power grids when one of the elements fails (completely or partially) and shifts its load to nearby elements in the system. This failure process cascades through the elements of the system like a ripple on a pond and continues until substantially all of the elements in the system are compromised and/or the system becomes functionally disconnected from the source of its load. Examples[edit] History[edit]
Emergence In philosophy, systems theory, science, and art, emergence is a process whereby larger entities, patterns, and regularities arise through interactions among smaller or simpler entities that themselves do not exhibit such properties. Emergence is central in theories of integrative levels and of complex systems. For instance, the phenomenon life as studied in biology is commonly perceived as an emergent property of interacting molecules as studied in chemistry, whose phenomena reflect interactions among elementary particles, modeled in particle physics, that at such higher mass—via substantial conglomeration—exhibit motion as modeled in gravitational physics. Neurobiological phenomena are often presumed to suffice as the underlying basis of psychological phenomena, whereby economic phenomena are in turn presumed to principally emerge. In philosophy, emergence typically refers to emergentism. In philosophy[edit] Main article: Emergentism Definitions[edit] Strong and weak emergence[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
Complex system This article largely discusses complex systems as a subject of mathematics and the attempts to emulate physical complex systems with emergent properties. For other scientific and professional disciplines addressing complexity in their fields see the complex systems article and references. A complex system is a damped, driven system (for example, a harmonic oscillator) whose total energy exceeds the threshold for it to perform according to classical mechanics but does not reach the threshold for the system to exhibit properties according to chaos theory. History[edit] Although it is arguable that humans have been studying complex systems for thousands of years, the modern scientific study of complex systems is relatively young in comparison to conventional fields of science with simple system assumptions, such as physics and chemistry. Types of complex systems[edit] Chaotic systems[edit] For a dynamical system to be classified as chaotic, it must have the following properties:[2]
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. The concept of self-organization is central to the description of biological systems, from the subcellular to the ecosystem level. 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] Examples[edit]
Chaos theory A double rod pendulum animation showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a completely different trajectory. The double rod pendulum is one of the simplest dynamical systems that has chaotic solutions. Chaos: When the present determines the future, but the approximate present does not approximately determine the future. Chaotic behavior can be observed in many natural systems, such as weather and climate.[6][7] This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps. Introduction[edit] Chaos theory concerns deterministic systems whose behavior can in principle be predicted. Chaotic dynamics[edit] The map defined by x → 4 x (1 – x) and y → x + y mod 1 displays sensitivity to initial conditions. In common usage, "chaos" means "a state of disorder".[9] However, in chaos theory, the term is defined more precisely. where , and , is: .
Black box System where only the inputs and outputs can be viewed, and not its implementation In science, computing, and engineering, a black box is a system which can be viewed in terms of its inputs and outputs (or transfer characteristics), without any knowledge of its internal workings. Its implementation is "opaque" (black). The term can be used to refer to many inner workings, such as those of a transistor, an engine, an algorithm, the human brain, or an institution or government. History[edit] In cybernetics, a full treatment was given by Ross Ashby in 1956.[4] A black box was described by Norbert Wiener in 1961 as an unknown system that was to be identified using the techniques of system identification.[5] He saw the first step in self-organization as being to be able to copy the output behavior of a black box. Systems theory[edit] The constitution and structure of the box are altogether irrelevant to the approach under consideration, which is purely external or phenomenological. (...)
039;s Center for Social Dynamics and Complexity November 5-6, 2010 2010 Computational Social Science Society Conference September 30 - October 2, 2010 IASC North American Regional Meeting CSDC joins the Consortium for Biosocial Complex Systems Together with the Center for Institutional Diversity and the Mathematical, Computational, and Modeling Sciences Center, the CSDC has been brought into the Consortium for Biosocial Complex Systems under the leadership of Sander van der Leeuw. "Integration is the key to being a leader in solving complex challenges," van der Leeuw says. The new Consortium is also a part of the university-wide Complex Adaptive Systems Initiative headed by Sander van der Leeuw and George Poste.
Attractiveness principle Attractiveness Principle is one of System Dynamics archetypes. System archetypes describe common patterns of behavior in dynamic complex systems. Attractiveness principle is a variation of Limits to Growth archetype, with restrictions caused by multiple limits. The limiting factors here are each of different character and usually cannot be dealt with the same way and/or (and very likely) they cannot be all addressed. Introduction to the problem[edit] Attractiveness principle is a concept that incorporates the fact that any product or kind of business cannot ever be “all things to all people” [1] though companies very often strive to follow this way.[2] One needs to make necessary decisions on the characteristics of the product as it cannot be perfect in all dimensions. Application field[edit] Knowledge of the attractiveness principle system archetype is essential in management of various projects and businesses. History[edit] Model[edit] Structure[edit] Figure 1. Figure 2. Trade-offs[edit]