Our investigation was to study the feasibility of piece-wise synchronization of chaotic circuits. In conventional experiments of electronic-circuit chaotic synchronization, two circuits were real-time and continuous connected together. In our research, a computer was used as the master subsystem that output chaotic signals to a slave circuit to study the performance of synchronization. The circuit was based on Cuomo¡¦s design. Several methods of piece-wise control were tested to find out the key point of chaotic synchronization. The experimental results revealed that the most important synchronized waveforms were the chaotic orbits near the region that the attractor change quadrants. A conditional piece-wise synchronization method was developed based on our discoveries. Comparing to the periodic piece-wise synchronization method, our method is more robust to sustain the circuit noise. Another advantage is that, in our method, the experimental results fit the computer simulation quite well.

Würzburg, Univ., Diss., 2005

Univ., Diss.--Düsseldorf.

Diss.--Soziologie--Saarbrücken, 1979. / Bibliogr. p. 411-435.

Lorenz curves are extensively used in economics to analyze income inequality metrics. In this thesis, we discuss confidence interval estimation methods for generalized Lorenz curve. We first obtain normal approximation (NA) and empirical likelihood (EL) based confidence intervals for generalized Lorenz curves. Then we perform simulation studies to compare coverage probabilities and lengths of the proposed EL-based confidence interval with the NA-based confidence interval for generalized Lorenz curve. Simulation results show that the EL-based confidence intervals have better coverage probabilities and shorter lengths than the NA-based intervals at 100p-th percentiles when p is greater than 0.50. Finally, two real examples on income are used to evaluate the applicability of these methods: the first example is the 2001 income data from the Panel Study of Income Dynamics (PSID) and the second example makes use of households’ median income for the USA by counties for the years 1999 and 2006

<p>In 1998 the Swedish mathematician Warwick Tucker used rigorous interval arithmetic and normal form theory to prove the existence of a strange attractor in the Lorenz system. In large parts, that proof consists of computations implemented and performed on a computer. This thesis is an independent numerical verification of the result obtained by Warwick Tucker, as well as a study of a higher-dimensional system of ordinary differential equations introduced by the Swedish physicist Lennart Stenflo.</p><p>The same type of mapping data as Warwick Tucker obtained is calculated here via a combination of numerical integration, solving optimisation problems and a coordinate change that brings the system to a normal form around the stationary point in the origin. This data is collected in a graph and the problem of determining the existence of a strange attractor is translated to a few graph theoretical problems. The end result, after the numerical study, is a support for the conclusion that the attractor set of the Lorenz system is a strange attractor and also for the conclusion that the Lorenz-Stenflo system possesses a strange attractor.</p>

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In 1998 the Swedish mathematician Warwick Tucker used rigorous interval arithmetic and normal form theory to prove the existence of a strange attractor in the Lorenz system. In large parts, that proof consists of computations implemented and performed on a computer. This thesis is an independent numerical verification of the result obtained by Warwick Tucker, as well as a study of a higher-dimensional system of ordinary differential equations introduced by the Swedish physicist Lennart Stenflo. The same type of mapping data as Warwick Tucker obtained is calculated here via a combination of numerical integration, solving optimisation problems and a coordinate change that brings the system to a normal form around the stationary point in the origin. This data is collected in a graph and the problem of determining the existence of a strange attractor is translated to a few graph theoretical problems. The end result, after the numerical study, is a support for the conclusion that the attractor set of the Lorenz system is a strange attractor and also for the conclusion that the Lorenz-Stenflo system possesses a strange attractor. / QC 20101007

Thesis--Cologne. / Vita. Includes bibliographical references (p. 241-265).

Thesis (S.T.D.)--Concordia Seminary, St. Louis, Missouri, 1994. / This is an electronic reproduction of TREN, #020-0117. Includes bibliographical references (leaves 213-217).