Lyapunov Exponents

Lyapunov Exponents

A measure of the dynamics of an attractor. Each dimension has a Lyapunov exponent. A positive exponent measures sensitive dependence on initial conditions, or how much our forecasts can diverge based upon different estimates of starting conditions. Another way to view Lyapunov exponents is the loss of predictive ability as we look forward into time. Strange Attractors are characterized by at least one positive exponent. A negative exponent measures how points converge towards one another. Point Attractors are characterized by all negative variables. See: Attractor, Limit Cycle, Point Attractor, Strange Attractor.
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2005) 'Recurrent neural networks employing Lyapunov exponents for EEG signals classification', Expert Systems with Applications, Vol.
Then he defines the Lyapunov exponents of such a co-cycle with respect to a harmonic probability measure directed by the lamination, and provides an Oseledec multiplicative ergodic theorem in this context.
It is well known that every ergodic measure whose Lyapunov exponents are all negative of a [C.
Whether this type of an attracting set could possess chaotic features is an issue that depends further on the denseness property and the existence of positive Lyapunov exponents, which maybe specific to each individual model, physical parameterization, boundary treatments, or model vertical and horizontal resolution.
Characteristic Lyapunov exponents and smooth ergodic theory," Russian Math.
It means that the Perron and Lyapunov exponents of the solution [(x(n, [x.
In the context of the current paper it is worth noting that the theoretical results regarding the linear magnetic dynamos at sub-Kolmogorov scale rely upon the Lyapunov exponents of chaotic flows (cf.
Power system transient stability analysis via the concept of Lyapunov Exponents.
Their topics include terminology and definitions of dynamical systems, the Frobenius-Perron operator and infinitesimal generator, graph partition methods and their relationship to transport in dynamical systems, the topological dynamics perspective of symbol dynamics, and finite-time Lyapunov exponents.
Maximum Lyapunov exponents as predictors of global gait stability: a modelling approach.
Cases that did not have at least 100 points were excluded from the study, as required when using techniques such as recurrence plots and Lyapunov exponents (Heath, 2000).
The results demonstrated that the average Lyapunov exponents for the conventional, pineapple, and chaos screw elements are 0.