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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 double-rod pendulum is one of the simplest dynamical systems with chaotic solutions. 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.
In the OGY method, small, wisely chosen, kicks are applied to the system once per cycle, to maintain it near the desired unstable periodic orbit. [3] To start, one obtains information about the chaotic system by analyzing a slice of the chaotic attractor. This slice is a Poincaré section. After the information about the section has been ...
The system becomes more chaotic as dynamical symmetries are broken by increasing the quantum defect; consequently, the distribution evolves from nearly a Poisson distribution (a) to that of Wigner's surmise (h). Statistical measures of quantum chaos were born out of a desire to quantify spectral features of complex systems.
A coupled map lattice (CML) is a dynamical system that models the behavior of nonlinear systems (especially partial differential equations).They are predominantly used to qualitatively study the chaotic dynamics of spatially extended systems.
Chaotic maps often occur in the study of dynamical systems. Chaotic maps and iterated functions often generate fractals . Some fractals are studied as objects themselves, as sets rather than in terms of the maps that generate them.
The Tinkerbell map is a discrete-time dynamical system ... Chaos: An Introduction to Dynamical Systems, ... is Chaotic" SIAM J. Applied Dynamical Systems 10, n.4 1480 ...
Recent research has shown how chaotic computers can be recruited in fault tolerant applications, by introduction of dynamic based fault detection methods. [6] Also it has been demonstrated that multidimensional dynamical states available in a single ChaoGate can be exploited to implement parallel chaos computing, [7] [8] and as an example, this parallel architecture can lead to constructing an ...
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