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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]
As a pedagogic tool, the Malkus waterwheel became a paradigmatic realization of a chaotic system, and is widely used in the teaching of chaos theory. [3] In addition to its pedagogic use, the Malkus waterwheel has been actively studied by researchers in dynamical systems and chaos. [4] [5] [6] [7]
Shaw was one of the pioneers of chaos theory and his work at University of California, Santa Cruz on the subject was among the first research into the relationship between predictable motion and chaos in a landmark PhD thesis. [3] He was part of the Dynamical Systems Collective with J. Doyne Farmer, Norman Packard, and James Crutchfield. The ...
Devaney is known for formulating a simple and widely used definition of chaotic systems, one that does not need advanced concepts such as measure theory. [8] In his 1989 book An Introduction to Chaotic Dynamical Systems, Devaney defined a system to be chaotic if it has sensitive dependence on initial conditions, it is topologically transitive (for any two open sets, some points from one set ...
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 ...
Guanrong Chen (陈关荣) or Ron Chen [1] is a Chinese mathematician who made contributions to Chaos theory.He has been the chair professor and the founding director of the Centre for Chaos and Complex Networks at the City University of Hong Kong since 2000.
[3] [4] He is known for his work on nonlinear systems, including contributions to the study of synchronization in dynamical systems, and for his research in a variety of areas of applied mathematics, including mathematical biology and complex network theory. Strogatz is the host of Quanta Magazine's The Joy of Why podcast. [5]
Recurrence quantification analysis (RQA) is a method of nonlinear data analysis (cf. chaos theory) for the investigation of dynamical systems. It quantifies the number and duration of recurrences of a dynamical system presented by its phase space trajectory.