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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.
MIT scientists discovered particles transition from chaos to order due to entropy. This breakthrough reveals hidden dynamics of collective motion in systems.
The name for this phenomenon is "Adaptation to the edge of chaos". Adaptation to the edge of chaos refers to the idea that many complex adaptive systems (CASs) seem to intuitively evolve toward a regime near the boundary between chaos and order. [19] Physics has shown that edge of chaos is the optimal settings for control of a system. [20]
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.
“Chaos is a fact of life … and a part of dynamical systems theory,” Lin explains to Popular Mechanics in an email. “Some systems are inherently chaotic, while others are not.
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 ...
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 ...