Mathematics Subject Classifications (1991): 39xx, 92Bxx, 35xx Library of Congress Cataloging-in-Publication Data Kaplan, Daniel, 1959-Understanding nonlinear dynamics I Daniel Kaplan and Leon Glass. p. cm. -(Texts in applied mathematics; 19) Includes bibliographica1 references and index.

Biomedical signals often vary in a complex and irregular manner. Analysis of variability in such signals generally does not address directly their complexity, and so may miss potentially useful information. We analyze the complexity of heart rate and beat-to-beat blood pressure using two methods motivated by nonlinear dynamics (chaos theory). A comparison of a group of healthy elderly subjects with healthy young adults indicates that the complexity of cardiovascular dynamics is reduced with aging. This suggests that complexity of variability may be a useful physiological marker.

Mathematics Subject Classifications (1991): 39xx, 92Bxx, 35xx Library of Congress Cataloging-in-Publication Data Kaplan, Daniel, 1959-Understanding nonlinear dynamics I Daniel Kaplan and Leon Glass. p. cm. -(Texts in applied mathematics; 19) Includes bibliographica1 references and index.

No abstract

Interest has been growing in testing for nonlinearity or chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We designed and ran a single-blind controlled competition among five highly regarded tests for nonlinearity or chaos with ten simulated data series. The data generating mechanisms include linear processes, chaotic recursions, and nonchaotic stochastic processes; and both large and small samples were included in the experiment. The data series were produced in a single blind manner by the competition manager and sent by e-mail, without identifying information, to the experiment participants. Each such participant is an acknowledged expert in one of the tests and has a possible vested interest in producing the best possible results with that one test. The results of this competition provide much surprising information about the power functions of some of the best regarded tests for nonlinearity or noisy chaos.