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Some examples of Lyapunov times are: chaotic electrical circuits, about 1 millisecond; weather systems, a few days (unproven); the inner solar system, 4 to 5 million years. [19] In chaotic systems, the uncertainty in a forecast increases exponentially with elapsed time.
Burke-Shaw chaotic attractor [8] continuous: real: 3: 2: Chen chaotic attractor [9] continuous: real: 3: 3: Not topologically conjugate to the Lorenz attractor. Chen-Celikovsky system [10] continuous: real: 3 "Generalized Lorenz canonical form of chaotic systems" Chen-LU system [11] continuous: real: 3: 3: Interpolates between Lorenz-like and ...
This category includes examples of dynamical systems that are ergodic, mixing, or otherwise exhibit chaotic behavior. Subcategories This category has only the following subcategory.
Deterministic system (mathematics) Linear system; Partial differential equation; Dynamical systems and chaos theory; Chaos theory. Chaos argument; Butterfly effect; 0-1 test for chaos; Bifurcation diagram; Feigenbaum constant; Sharkovskii's theorem; Attractor. Strange nonchaotic attractor; Stability theory. Mechanical equilibrium; Astable ...
In dynamical system, the Koopman operator is a natural linear operator on the space of scalar fields. For general nonlinear systems, the eigenfunctions of this operator cannot be expressed in any nice form. Instead one must compute them numerically. These modes can give insight into the symbolic dynamics of chaotic maps like the Hénon map. [7]
In lab experiments that study chaos theory, approaches designed to control chaos are based on certain observed system behaviors. Any chaotic attractor contains an infinite number of unstable, periodic orbits. Chaotic dynamics, then, consists of a motion where the system state moves in the neighborhood of one of these orbits for a while, then ...
A hyperchaotic system is a dynamical system with a bounded attractor set, on which there are at least two positive Lyapunov exponents. [ 1 ] Since on an attractor, the sum of Lyapunov exponents is non-positive, there must be at least one negative Lyapunov exponent.
The general study of chaotic quantum systems is known as quantum chaos. A particularly striking example of scarring on an elliptical table is given by the observation of the so-called quantum mirage .