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.
References in periodicals archive ?
Maximum Lyapunov exponents as predictors of global gait stability: a modelling approach.
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.
The results demonstrated that the average Lyapunov exponents for the conventional, pineapple, and chaos screw elements are 0.
9:45 LYAPUNOV EXPONENTS AND THE INVARIANT DENSITY RECONSTRUCTION OF CHAOTICMAPS: A SWARM INTELLIGENCE APPROACH
The Lyapunov exponents indicate chaos when the largest exponent is positive.
Since the Lyapunov exponents are not required for the calculation, the nonlinear controller is effective and convenient to synchronize two identical systems and two different chaotic systems.
The dynamical behavior of the system (2) can be characterized with its Lyapunov exponents which are computed numerically.
9-11,39,40,45] for stability theory, Lyapunov exponents, and all that).
In this new treatment of one of the most dynamic but difficult topics in modern theory, Chernov and Markarian keep the beginner in mind as they start from the basics and work through all the definitions and give full proofs of the main theorems as they cover basic constructions, Lyapunov exponents and hyperbolicity, dispersing billiards, dynamics of unstable manifolds, ergodic properties, statistical properties, Bunimovich billiards and general focusing chaotic billiards.
This paper examines the efficacy of the statistical measures of risk in the light of results obtained from the analysis of stock market data using contemporary techniques of mathematical modelling of dynamical systems like the Rescaled Range Analysis and the related Hurst's Exponent, Fractal Dimensions, and the Lyapunov Exponents.
Lyapunov exponents give valuable information about long term dynamics.