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Finite-dimensional linear systems are never chaotic; for a dynamical system to display chaotic behavior, it must be either nonlinear or infinite-dimensional. The Poincaré–Bendixson theorem states that a two-dimensional differential equation has very regular behavior.
Download as PDF ; Printable version; In other projects ... From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Chaos theory; Retrieved from "https://en ...
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. This is often because there are several different iterative procedures that generate the same fractal.
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 ...
From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Chaos theory
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 ...
This category includes examples of dynamical systems that are ergodic, mixing, or otherwise exhibit chaotic behavior. Subcategories This category has only the following subcategory.
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 ...