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Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. [2]
In Landau theory, the development of order in the everyday sense coincides with the change in the value of a mathematical quantity, a so-called order parameter. An example of an order parameter for crystallization is "bond orientational order" describing the development of preferred directions (the crystallographic axes) in space.
The phrase edge of chaos was coined in the late 1980s by chaos theory physicist Norman Packard. [7] [8] In the next decade, Packard and mathematician Doyne Farmer co-authored many papers on understanding how self-organization and order emerges at the edge of chaos. [7]
The Origins of Chaos Theory. While Lorenz might be known for coining the “Butterfly Effect” in relation to chaos theory, Lin says that the discovery of chaos theory actually dates back to the ...
Spontaneous order, also named self-organization in the hard sciences, is the spontaneous emergence of order out of seeming chaos. The term "self-organization" is more often used for physical changes and biological processes, while "spontaneous order" is typically used to describe the emergence of various kinds of social orders in human social networks from the behavior of a combination of self ...
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The term is closely associated with the work of the mathematician and meteorologist Edward Norton Lorenz.
Besides structural order, one may consider charge ordering, spin ordering, magnetic ordering, and compositional ordering. Magnetic ordering is observable in neutron diffraction. It is a thermodynamic entropy concept often displayed by a second-order phase transition. Generally speaking, high thermal energy is associated with disorder and low ...
By comparison, based on the concept of attractor coexistence within the generalized Lorenz model [26] and the original Lorenz model ([36] [37]), Shen and his co-authors [35] [38] proposed a revised view that “weather possesses both chaos and order with distinct predictability”. The revised view, which is a build-up of the conventional view ...