In this paper, we study the Lyapunov exponents of a micro chaotic mixer to understand the mixing effectiveness under different operating parameters. A simple kinematic micro mixer model is used for the simulated flow visualization and then for the computation of Lyapunov exponents using two different numerical methods. These two methods generate consistent result to corroborate the existence of...

Modeling and analysis of future prices has been hot topic for economic analysts in recent years. Traditionally, the complex movements in the prices are usually taken as random or stochastic process. However, they may be produced by a deterministic nonlinear process. Accuracy and efficiency of economic models in the short period forecasting is strategic and crucial for business world. Nonlinear ...

Lyapunov exponents are an important concept to describe qualitative properties of dynamical systems. For instance, chaotic systems can be caracterized with the positivity of the largest Lyapunov exponent. In this paper, we use the Iwasawa decomposition of the semisimple Lie group Sp(n,R) and the enlargement of the phase space to give a theoretical computation of Lyapunov exponents of almost per...

We suggest to present a discrete sequence of cardiointervals in the form of a smooth time dependence and for the given time series compute the largest Lyapunov exponent. Processing the database with RR-intervals of patients su€ering from coronary artery disease (CAD) has shown that the largest Lyapunov exponent can be a diagnostic criteria allowing one to distinguish between di€erent groups of ...

We analytically establish the role of a spectrum of Lyapunov exponents in the evolution of phase-space distributions r(p ,q). Of particular interest is l2 , an exponent that quantifies the rate at which chaotically evolving distributions acquire structure at increasingly smaller scales and is generally larger than the maximal Lyapunov exponent l for trajectories. The approach is trajectory inde...

The Lyapunov exponent for collective motion is defined in order to characterize chaotic properties of collective motion for large populations of chaotic elements. Numerical computations for this quantity suggest that such collective motion is always chaotic, whenever it appears. Chaotic behavior of collective motion is found to be confined within a small scale, whose size is estimated using the...

By tracking the divergence of two initially close trajectories in phase space in an Eulerian approach to forced turbulence, the relation between the maximal Lyapunov exponent λ and the Reynolds number Re is measured using direct numerical simulations, performed on up to 2048^{3} collocation points. The Lyapunov exponent is found to solely depend on the Reynolds number with λ∝Re^{0.53} and that ...

We provide a new proof of the theorem of Simon and Zhu that in the region |E| < λ for a.e. energies, − d2 dx2 + λ cos(xα), 0 < α < 1 has Lyapunov behavior with a quasi-classical formula for the Lyapunov exponent. We also prove Lyapunov behavior for a.e. E ∈ [−2, 2] for the discrete model with V (j2) = ej , V (n) = 0 if n / ∈ {1, 4, 9, . . . }. The arguments depend on a direct analysis of the eq...

using nonlinear mathematical analysis, on the data obtained for.time seriesof shahd-iran price during 3.5 years, the characteristics,of the process associated with this, is analysed. analysing the behaviour of the time series associated with returns is indicative ofits short-term predictability nature. however, employing analysis regarding the correlation dimension estimate. it is indicated tha...

Fault Detection in Dynamic Systems Using the Largest Lyapunov Exponent. (May 2011) Yifu Sun, B.S, Beijing Institute of Technology Chair of Advisory Committee: Dr. Alexander G. Parlos A complete method for calculating the largest Lyapunov exponent is developed in this thesis. For phase space reconstruction, a time delay estimator based on the average mutual information is discussed first. Then, ...