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Showing 1 to 20 of 46 for “"Lyapunov exponents."”.
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Lyapunov Exponents, Entropy and Dimension
We consider diffeomorphisms of a compact Riemann Surface. A development of Oseledec's Multiplicative Ergodic Theorem is given, along with a development of measure theoretic entropy and dimension. The main result, due to L.S. Young, is that for certain diffeomorphisms of a surface, there is a …
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Quantifying Dynamic Stability of Musculoskeletal Systems using Lyapunov Exponents
Increased attention has been paid in recent years to the means in which the body maintains stability and the subtleties of the neurocontroller. Variability of kinematic data has been used as a measure of stability but these analyses are not appropriate for quantifying stability of dynamic systems. …
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Computation of Lyapunov Exponents and Control of a Hyperchaotic System
… Chen system and also estimates the largest Lyapunov characteristic exponent (LCE) and provides a method to compute the entire Lyapunov spectrum of the dynamical system. The computation of the Lyapunov spectrum relies on calculating the order-p LCEs and repeated application of the …
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Statistical properties and scaling of the Lyapunov exponents in stochastic systems
… mit einer stochastischen Theorie für die Lyapunov-Exponenten befaßt sind. Mit Hilfe dieser Theorie werden universelle Skalengesetze untersucht, die in gekoppelten chaotischen und ungeordneten Systemen auftreten. Zunächst werden zwei zeitkontinuierliche stochastische Modelle für schwach …
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Biodynamic Analysis of Human Torso Stability using Finite Time Lyapunov Exponents
… First, the time series averaged finite time Lyapunov exponent is calculated from data obtained during seated stability experiments. The Lyapunov exponent is found to increase with increasing task difficulty. Second, a new metric for evaluating torso stability is introduced, the threshold of …
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Application of Lyapunov Exponents to Strange Attractors and Intact & Damaged Ship Stability
… stability. This research presents the use of Lyapunov exponents, a quantity that measures the rate of trajectory separation in phase space, to predict capsize events for both intact and damaged stability cases. The algorithm searches backwards in ship motion time histories to gather …
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Lyapunov Exponents and Invariant Manifold for Random Dynamical Systems in a Banach Space
<p>We study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. We prove a multiplicative ergodic theorem. Then, we use this …
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Thermal stability criteria embedded in avanced control systems for batch process intensification
… networks based on the divergence criterion. Lyapunov exponents are an alternative method to predict thermal runaway behaviour. Embedding thermal stability criteria within Model Predictive Control (MPC) frameworks results in advanced control systems capable of intensifying batch processes …
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Eine hybride Methode zur Berechnung von Liapunow-Exponenten
… a new numerical method for computing some or all Lyapunov exponents of a discrete dynamical system. It is called hybrid because it combines the classical QR method with more recent methods that use spatial integration with respect to an invariant ergodic measure. We also investigate error …
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The Complex Spatiotemporal Dynamics of a Shallow Fluid Layer
… field is obtained as well as the spectrum of Lyapunov exponents and Lyapunov vectors. The Lyapunov exponents and their corresponding perturbation fields are used to determine when and where events occur that contribute most to the chaotic dynamics. Roll pinch-off and roll mergers are found to …
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Determination of Three Dimensional Time Varying Flow Structures
… studying these flow structures is finite time Lyapunov exponents (FTLEs). These exponents can reveal regions in the fluid, referred to as Lagragnian coherent structures (LCSs), where fluid elements diverge or attract. Better knowledge of how these time varying structures behave can greatly …
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ΓΕΝΙΚΑ ΚΑΙ ΤΟΠΙΚΑ ΧΑΡΑΚΤΗΡΙΣΤΙΚΑ ΤΗΣ ΧΑΟΤΙΚΗΣ ΔΟΜΗΣ ΘΑΛΑΣΣΙΩΝ ΔΥΝΑΜΙΚΩΝ ΣΥΣΤΗΜΑΤΩΝ
… UNDERLYING SYSTEM ATTRACTOR AND WE COMPUTE ITS LYAPUNOV EXPONENTS. DIMENSION ESTIMATES INDICATE THAT THE DYNAMICS CAN BE EXPLAINED BY A LOW- DIMENSIONAL DETERMINISTIC DYNAMICAL SYSTEM. LYAPUNOV EXPONENT ESTIMATES FURTHER SUBSTANTIATE THEABOVE CONCLUSION WHILE AT THE SAME TIME INDICATE THAT THE …
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Perturbation theory for the topological pressure in analytic dynamical systems
… dynamical indices, such as dimension spectra, Lyapunov exponents, escape rates and Renyi entropies inherit the real-analyticity in ~ from (I,M).
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Computational Intelligence and Complexity Measures for Chaotic Information Processing
… in computing algorithmic complexity measures, Lyapunov exponents, information dimension and topological entropy. These metrics are implemented to characterize the dynamic patterns of discrete and continuous systems. These metrics make it possible to distinguish order from disorder in these …
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Mathematical modelling and brain dynamical networks
… the stability of the HR system and compute its Lyapunov exponents (LEs). We consider coupled general sections of the HR system to create an undirected brain dynamical network (BDN) of Nn neurons. Then, we study the concepts of upper bound of mutual information rate (MIR) and synchronisation …
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Characterisation of local properties and prediction in chaotic dynamical systems
… This is done using two kinds of local exponents as well as ensemble studies. In conservative systems with trapping, the distribution of finite-time Lyapunov exponents (FTLE) has multiple maxima. These can be attributed to pieces of the trajectory that stay in the vicinity of islands of …
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Dinâmica e controle de caos de um sistema pendular com memória de forma
… All the behaviours are identified by their Lyapunov exponents. The extended time delay feedback technique is applied to control the system with two distinct types of controllers: a mechanical and a thermal. The stability of the orbits is identified using Floquet multipliers. Discussions …
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Extremes in events and dynamics : a nonlinear data analysis perspective on the past and present dynamics of the Indian summer monsoon
… the dynamical invariants such as dimension and Lyapunov exponents of the underlying system. A statistical test is also developed to estimate the significance of the identified transitions. Our method is justified by uncovering bifurcation structures in several paradigmatic models, providing more …
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Contraction analysis of nonlinear systems
… the heat equation, or the Schroedinger equation. Lyapunov exponents are not coordinate-invariant, and thus their exact physical meaning is somewhat questionable. As an alternative, we suggest an extension of linear eigenvalue analysis to nonlinear dynamic systems. Finally, the thesis derives new …
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Chaotic motions of nonlinearly moored structures
… phase portraits, spectra, Poincare maps, and Lyapunov exponents. The influence of various governing parameters on the response is examined. These include a dimensionless wave height, which characterizes the magnitude of the excitation; a relative wave frequency; and gap width and a …
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