A deterministic non-linear dynamic system that can produce random looking results. A chaotic system must have a fractal dimension, and exhibit sensitive dependence on initial conditions. See: Fractal Dimension, Lyapunov Exponent, Strange Attractor.
a fount of creation, transformation, and destruction.
Chaos is the breakdown of predictability, or a state of disorder.
Apparent disorder and confusion. A delicate balance the forces of stability and the forces of instability.
In chaos theory, a dynamical system that is neither static nor periodic.
Webster's dictionary (1988) defines chaos as "the disorder of formless matter and infinite space, supposed to have existed before the ordered universe", and "extreme confusion or disorder." In terms of systems, chaos is a state space (the condition of any system at a given time) where a system exhibits disorder, confusion, uncertainty, or instability.
Behavior of a dynamic system that has (a) a very large (possibly infinite) number of attractors and (b) is sensitive to initial conditions.
Whether Chaos is to be understood as a void or a primordial, formless, undifferentiated, and seething mass out of which the order of the universe is created, it is the starting point of creation. This unformed beginning is contrasted with later creation, a universe called the cosmos, a desgination meaning, literally, harmony or order. The sky and the stars, the earth and its creatures, and the laws and cycles which direct and control creation seem to exhibit the balance, order, and reason which the mind discerns in the natural world. For us chaos, together with its adjective chaotic, simply means a state of confusion. See cosmos.
A dynamical system is chaotic if it is bounded and sensitive to initial conditions. Both conditions are needed, because a simple linear map such as has positive Lyapunov exponent and is thus sensitive to initial conditions but is not chaotic, while bounded orbits that don't diverge from one another are too regular to be called `chaotic'. There is a more mathematically flavoured definition, usually attributed to Devaney, which uses transitivity. This is, to my mind, not the essence of chaos, though it allows precise discussion.
domain of inherent uncertainty and unpredictability; in the business context, may be partially concealed in aggregates such as demographic groups and mass-marketing, but at the individual level all real-world transactions involve some degree of chaos and complexity; also useful when deliberately invoked in creativity, in narrative and dialogue, and in foresight techniques such as scenario construction
the formless and disordered state of matter before the creation of the cosmos
(physics) a dynamical system that is extremely sensitive to its initial conditions
A system whose long term behaviour is unpredictable, tiny changes in the accuracy of the starting value rapidly diverge to anywhere in its possible state space. There can however be a finite number of available states, so statistical prediction can still be useful.
a state or condition which has no apparent orderly or predictable progression
The study of nonlinear dynamics (also called deterministic disorder).
is frequently defined as motion that displays "extreme sensitivity to inital conditions" (Kleppner, Ouabtum Chaos and the Bow-Stern Enigma, pp9-10 Physics today, Augus 1991)
(unpredictable and seemingly random behavior occurring in a system that sshould be governed by deterrministic laws. In such systems the equations that describe the way the system changes with time are non-linear and involve several variables. consequently, they are very sensitive to the initial conditions such that a very small initial difference may make enormous changes to the future state of the system. )
gap, chasm; disorder, formlessness, confusion, disorganization
n. Any condition of which the elements or parts are in utter disorder and confusion.
An approach to the study of systems enabled by computers which permit the study of systems over far more repetitions than hand held calculators or pencil and paper. Surprising behaviour emerged from these many repetitions. Seemingly simple systems behaved in unpredictable fashion and some exhibited radical differences in output from just minor variations in input. Systems thought to be stable could be seen to become unpredictably unstable. Chaos as it is mostly represented, however, is built upon a deterministic view of the universe. Thus it is held that when we are unable to predict the future of a system that does not mean anything random is going on, it just means we are unable to predict the future of a system.
a disordered state, lacking organization, confusing and unpredictable.
Property of a dynamic system that it is highly sensitive to small changes.
Complex and irregular (aperiodic) motions of a dynamical sytem that are characterized by a sensitivity to initial conditions. Chaotic systems often exhibit short term order, but seemingly longer term randomness with a broad band frequency spectrum.
Irregular motion of a dynamical system that is deterministic, sensitive to initial conditions, and impossible to predict in the long term with anything less than an infinite and perfect representation of analog values.
It is an unpredictable situation for observers and participants.
The property describing a dynamical system that exhibits erratic behavior in the sense that very small changes in the initial state of the system rapidly lead to large and apparently unpredictable changes in the later state.
Chaos (derived from the Greek , Chaos) typically refers to unpredictability, and is the antithetical concept of cosmos. The word did not mean "disorder" in classical-period ancient Greece. It meant "the primal emptiness, space" (see Chaos (mythology)).