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Showing 1 to 20 of 39 for “"Lyapunov exponent"”.

  1. Energy level statistics and Lyapunov exponent in the stadium billiard

    Gloss, David SamuelMassachusetts Institute of Technology1995

    Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Physics, 1995.

    mit Repository record

  2. Relating information-theoretic limits to the lyapunov exponent of a dynamical system

    Ebeid, Hani-James M.University of Illinois at Urbana-Champaign2010

    … coding with feedforward - and see that the Lyapunov exponent of a related dynamical system emerges as a fundamental quantity. For channel coding with feedback, we show that for a broad class of channels - both with and without memory - the Lyapunov exponent of the transmission function is …

    uiuc Repository record

  3. Nonlinear Behaviors Analysis and Nonlinear Characteristics Diagnosing of Mechanical Vibration Systems

    Xia, DandanFaculty of Graduate Studies and Research, University of Regina2016

    … a proposed method combining the P-R method and Lyapunov exponent method is established in this research. The Lyapunov exponent method is probably the most widely used method in diagnosing nonlinear behaviors of dynamic systems. However, in comparing with the P-R method, Lyapunov approach is …

    regina Repository record

  4. Stochastic stability and global bifurcations in gyroscopic mechanical systems

    Doyle, Monica MargaretUniversity of Illinois at Urbana-Champaign2011

    … stability is defined by the sign of the maximal Lyapunov exponent, the exponential growth rate of solutions to a linear stochastic system. Similarly, the moment stability of such a system is determined by the sign of the moment Lyapunov exponent which describes the exponential growth rate of the …

    uiuc Repository record

  5. An Investigation of Determinism and Chaotic Behavior in Flight Performance Data: A Chaos Theory and Nonlinear Time Series Analysis Approach

    Amanfu, Lionel Blankson

    … from non-stationary process. The Maximal Lyapunov Exponent (MLE) value which indicate chaotic behavior exist in the data revealed that most of the data examined possessed some traces of deterministic chaotic behavior evident by the low Maximal Lyapunov Exponent value.</p>

    embry-riddle Repository record

  6. Biodynamic Analysis of Human Torso Stability using Finite Time Lyapunov Exponents

    Tanaka, Martin L.Virginia Tech2008

    … 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 …

    vt Repository record

  7. Robust bifurcation behavior in the presence of external random excitation

    Leng, Gerard Siew BingUniversity of Illinois at Urbana-Champaign2011

    … mode only at the expense of the other. The Lyapunov exponent is then introduced as a quantitative measure of the robustness of the steady state response to small perturbations. It is found that while the Lyapunov exponent does not indicate the qualitative changes in the steady state …

    uiuc Repository record

  8. Machine tool chatter suppression using spindle speed variation

    Lingala, NishanthUniversity of Illinois at Urbana-Champaign2010

    … authors present asymptotic expansion for the top Lyapunov exponent of a scalar linear delay differential equation driven by a two state Markov process. We extend their result to a vector case. In the case when driving noise is small, we construct an asymptotic expansion for the top Lyapunov …

    uiuc Repository record

  9. ΓΕΝΙΚΑ ΚΑΙ ΤΟΠΙΚΑ ΧΑΡΑΚΤΗΡΙΣΤΙΚΑ ΤΗΣ ΧΑΟΤΙΚΗΣ ΔΟΜΗΣ ΘΑΛΑΣΣΙΩΝ ΔΥΝΑΜΙΚΩΝ ΣΥΣΤΗΜΑΤΩΝ

    Triantafyllou, George, Τριανταφύλλου, ΓεώργιοςAristotle University Of Thessaloniki (AUTH)1991

    … 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 …

    greece Repository record

  10. Development of new analytical techniques for chaotic time series

    Franchi, MatteoUniversità degli studi di Trento2015

    … properties of the finite-time maximum Lyapunov exponent determined out of a time series by using the divergent rate method. To reach this goal, we developed a new, completely automatic algorithm based on the method developed by Gao and Zheng. A main achievement of this part of the work …

    trento Repository record

  11. The parametrically excited pendulum and the criteria for predicting the onset of chaos

    Hsu, Tseng-HsingVirginia Tech1991

    … values for chaos are obtained by simulation. The Lyapunov exponent and the fast Fourier transform ( FFT ) are used as the criteria to determine if the system is chaotic. Two predictive theoretical criteria, the Melnikov criterion and a period-doubling criterion, are then applied to the system. The …

    vt Repository record

  12. The rotor-oscillator flow : searching for coherence amidst chaos

    Fay, Sarah (Sarah C.)Massachusetts Institute of Technology2015

    … by a sea of chaos. Through finite-time Lyapunov exponent (FTLE) analysis, a roughly optimal coupling was found. The parameters that describe this coupling are the nondimensional oscillation amplitude [epsilon] = 0.125 and frequency [lambda] = 0.4[pi]. In order to understand more about …

    mit Repository record

  13. Atmospheric Lagrangian transport structures and their applications to aerobiology

    Bozorg Magham, Amir EbrahimVirginia Tech2014

    … We apply powerful notions such as finite-time Lyapunov exponent (FTLE) and the associated Lagrangian coherent structures (LCS) and we attempt to provide mathematical explanations and frameworks for some applied questions which are based on realistic concerns of atmospheric transport phenomena. …

    vt Repository record

  14. Quantifying Spatio-Temporal Chaos in Rayleigh Bénard Convection

    Einarsson, Magnús IngiVirginia Tech2006

    … as its linearized solutions in order to obtain Lyapunov diagnostics. The emphasis is on the effects that the domain size Γ (gamma) has on the system dynamics (Γ = radius/depth for a cylindrical domain). Temperature fields were viewed for different Γ's) and a transition to spiral defect chaos was …

    vt Repository record

  15. Integrated regional enstrophy and its correlation with regime transitions in the Northern Hemisphere

    Klaus, Emily MarieUniversity of Missouri--Columbia2019

    … this quantity is correlated to the positive Lyapunov Exponent for hemispheric flow, and as such is a measure of flow stability or predictability. In this study, IRE is calculated at 500-hPa over an area that encompasses 0[degrees] to 70[degree]s N in the Northern Hemisphere. The data sets …

    missouri Repository record

  16. A numerical study on microbubble mixer

    Guo, LinUniversity of Illinois at Urbana-Champaign2014

    … using Poincare sections and the Finite-time Lyapunov exponent. These indicators provide evidence that by properly blinking between different streaming patterns, chaotic-like mixing can be created inside our mixer. The observation made from numerical results that the size of the region that is …

    uiuc Repository record

  17. Stochastic stability of power systems

    Chikkerur, VishalUniversity of Illinois at Urbana-Champaign2018

    … Dynamical Systems (RDS) perspective. The maximal Lyapunov exponent (MLE) for a two dimensional model of a synchronous generator is calculated analytically to account for multiple white noise forcing elements. The ``real"" or colored noise case is also considered and an analytic expression derived. …

    uiuc Repository record

  18. Influence of external environment on fluid/ion transport in confined nanoscale systems

    Nandigana, Vishal Venkata RaghaveUniversity of Illinois at Urbana-Champaign2016

    … quantify chaos in terms of maximum Lyapunov exponent. The maximum Lyapunov exponent increases monotonically with an increase in the applied bias voltage and the macropore reservoir diameter. Furthermore, I postulate a low frequency ""1/f"" type dynamics for the voltage dominated …

    uiuc Repository record

  19. Identifying dynamical boundaries and phase space transport using Lagrangian coherent structures

    Tallapragada, PhanindraVirginia Tech2010

    … qualitatively different fates. The finite-time Lyapunov exponent (FTLE) method is a general and equation-free method that identifies codimension-one sets which have a locally high rate of stretching around which maximal exponential expansion of line elements occurs. These codimension-one sets …

    vt Repository record

  20. Chaotic behavior and energy polarisation in flatband lattice models

    Cheong, Su HoDepartment of Mathematics and Applied Mathematics2023

    … and ∝ t0.5), is a chaotic process whose maximum Lyapunov exponent respectively decreases ∝ t−0.25 and ∝ t−0.3. By decreasing the system's disorder strength we alter the width of the bandgap, something which does not ap- pear to affect the spreading dynamics in the weak chaos regime, while our …

    cape-town Repository record

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