## Systems theory

In the physical sciences, an active transformation is one which actually changes the physical state of a system and makes sense even in the absence of a coordinate system whereas a passive transformation is merely a change in the coordinate system of no physical significance. The distinction between active and passive transformations is one which should always be kept in mind when working with transformations. By default, by transformation, mathematicians usually mean passive transformations, while physicists could mean either. ...more on Wikipedia about "Active and passive transformation"

An adaptive system is a system that is able to adapt its behavior according to changes in its environment or in parts of the system itself. A human being, for instance, is certainly an adaptive system; so are organizations and families. Some man-made systems can be made adaptive as well; for instance, control systems utilize feedback loops in order to sense conditions in their environment and adapt accordingly. Robots incorporate many of these control systems. Neural Networks are a common type of algorithmic implementation of adaptive systems. ...more on Wikipedia about "Adaptive system"

Allopoiesis is the process whereby a system produces something other than the system itself. One example of this is an assembly line, where the final product (such as a car) is distinct from the machines doing the producing. This is in contrast with autopoiesis. ...more on Wikipedia about "Allopoiesis"

An anticausal system is a system with outputs and internal states that depend solely on future input values. An acausal system is a system that is not a causal system, that is one that depends on some future input values and possibly on some input values from the past or present. This is in contrast to a causal system which depends only on current and/or past input values. This is often a topic of control theory and digital signal processing (DSP). ...more on Wikipedia about "Anticausal system"

Autopoiesis literally means "auto (self)-creation" (from the Greek: auto - αυτό for self- and poiesis - ποίησις for creation or production) and expresses a fundamental complementarity between structure and function. The term was originally introduced by Chilean biologists Francisco Varela and Humberto Maturana in the early 1970s: ...more on Wikipedia about "Autopoiesis"

In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry. ...more on Wikipedia about "Catastrophe theory"

A causal system is a system with output and internal states that depends only on the current and previous input values. This property is referred to as causality. A system that has some dependence on input values from the future (in addition to possible past or current input values) is termed an acausal system, and a system that depends solely on future input values is an anticausal system. ...more on Wikipedia about "Causal system"

An Isolated system, is a physical system that does not interact with its surroundings. It obeys a number of conservation laws: its total energy and mass stay constant. They cannot enter or exit, but can only move around inside. An example is in the study of spacetime, where it is assumed that asymptotically flat spacetimes exist. ...more on Wikipedia about "Closed system"

Many natural phenomena can be considered to be complex systems, and their study (complexity science) is highly interdisciplinary. Examples of complex systems include ant-hills, ants themselves, human economies, nervous systems, cells and living things - especially human beings. ...more on Wikipedia about "Complex system"

Complexity, Problem Solving, and Sustainable Societies is an extremely influential 1996 paper in energy economics by Joseph Tainter. ...more on Wikipedia about "Complexity, Problem Solving, and Sustainable Societies"

Cybernetics is the study of communication and control, typically involving regulatory feedback, in living beings and machines, and in combinations of the two (eg. sociotechnical systems). ...more on Wikipedia about "Cybernetics"

Decentralized systems in systems theory are naturally-occurring, usually self-regulating systems found which function without an organized center or authority. A system that is decentralised lacks a nuclear body or center of control, and is commonly composed of many components which work in unison, and together form a stable structure. ...more on Wikipedia about "Decentralised system"

A dissipative system (or dissipative structure) is an open system which is operating far from thermodynamic equilibrium within an environment that exchanges energy, matter or entropy. A dissipative system is characterized by the spontaneous appearance of a complex, sometimes chaotic, structure. The term dissipative structures was coined by Ilya Prigogine. It is also called steady-state open system and nonequilibrium open system. ...more on Wikipedia about "Dissipative system"

Distributed parameter system (as opposed to a lumped parameter system) refers to a system whose state space is infinite- dimensional. A body whose state is heterogenous has a distributed parameter. It is usually described by partial differential equations. ...more on Wikipedia about "Distributed parameter systems"

A dynamic equilibrium will form if, at a given temperature, two reversible processes occur at the same rate. Many processes (such as chemical reactions) are reversible. ...more on Wikipedia about "Dynamic equilibrium"

The term eco-evolution was coined by Donella Meadows to describe "the power to add, change, evolve, or self-organize system structure" which she described as the fourth most powerful way to intervene in a system: ...more on Wikipedia about "Eco-evolution"

The generative sciences (or generative science) are the interdisciplinary and multidisciplinary sciences that explore the natural world and its complex behaviours as a generative process. Generative science shows how deterministic and finite rules and parameters in the natural phenomena interact with each other to generate indeterministic and infinite behaviour. ...more on Wikipedia about "Generative sciences"

The global brain is the name given to the emerging intelligent network formed by all people on Earth, together with the computers and communication links that connect them together. Like a real brain, this network is an immensely complex, self-organizing system, that processes information, makes decisions, solves problems, learns new connections and discovers new ideas. It plays the role of a collective nervous system for the whole of humanity. No person, organization or computer is in control of this system: its "thought" processes are distributed over all its components. ...more on Wikipedia about "Global brain"

In systems theory and linear algebra, a Gramian matrix is a real-valued symmetric matrix that can be used to test for linear independence of functions. The Gramian matrix of a set of functions $\\left\{l_i\left(\cdot\right),\,i=1,\dots,n\\right\}$ is defined as ...more on Wikipedia about "Gramian matrix"

Hierarchical systems theory involves the self alignment, or autopoiesis of a single system which continually passes successive states of chaotic phase transition through the constant and steady input of energy. Some would consider the hierarchies as being individually discrete systems, ignoring the evidence that each system has a hierarchical relationship to the one both above and below it, often having to do with the passing of energy from one state to the next, or the appearance of anti- entropic complexity. ...more on Wikipedia about "Hierarchical system theory"

Holism in science, or Holistic science, is a scientific paradigm that emphasizes the study of complex systems. Not a scientific discipline itself, it defines a philosophical lens by which emergence is taken into account when applying the scientific method, often within a wider interdisciplinary or multidisciplinary mode of inquiry. This practice is in contrast to a purely analytic tradition (sometimes called reductionism) which proports to understand systems by dividing them into their smallest possible or discernible elements and understanding their elemental properties alone. The holism/reductionism dichotomy is often evident in conflicting interpretations of experimental findings and in setting priorities for future research. ...more on Wikipedia about "Holism in science" Made by www.shortopedia.com. Systems_theory

Homeorhesis, derived from the Greek for "similar flow", is a concept encompassing dynamical systems which return to a trajectory, as opposed to systems which return to a particular state, which is termed homeostasis. ...more on Wikipedia about "Homeorhesis"

Homeostasis is the property of an open system, especially living organisms, to regulate its internal environment to maintain a stable, constant condition, by means of multiple dynamic equilibrium adjustments, controlled by interrelated regulation mechanisms. The term was coined in 1932 by Walter Cannon from the Greek homo (same, like) and stasis (to stand, posture). ...more on Wikipedia about "Homeostasis"

Whether a particular signal in a given system is seen as discrete or continuous, is ultimately a modeling question. So, a more accurate (still informal) description would be: a hybrid model of a system consists of both discrete signals (or variables) and continuous signal or variables. ...more on Wikipedia about "Hybrid system"

Hysteresis is a property of systems (usually physical systems) that do not instantly follow the forces applied to them, but react slowly, or do not return completely to their original state: that is, systems whose states depend on their immediate history. For instance, if you push on a piece of putty it will assume a new shape, and when you remove your hand it will not return to its original shape, or at least not immediately and not entirely. The term derives from an ancient Greek word meaning 'deficiency'. The phenomenon was identified, and the term coined, by Sir James Alfred Ewing in 1890. ...more on Wikipedia about "Hysteresis"