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Chaotic Dynamics (chaotic + dynamics)
Selected AbstractsCHAOTIC DYNAMICS OF FINANCING INVESTMENTMETROECONOMICA, Issue 1 2005Soumya Datta ABSTRACT The paper introduces the financial sector in a standard multiplier-accelerator framework by incorporating financial variables in the investment function. The resultant equation is similar in form to that of a logistic map, and hence behaves unpredictably under certain values of the parameters. Since monetary authorities have a large influence on many of these parameters, monetary policies are effective in both controlling investment and preventing or postponing a financial crisis. The monetary authorities, however, are also keen to play an additional role of keeping the system predictable. Under certain conditions, there could be a conflict between these two objectives,of preventing a financial crisis and keeping the system predictable. [source] Food web complexity and chaotic population dynamicsECOLOGY LETTERS, Issue 3 2002Gregor F. Fussmann Abstract In mathematical models, very simple communities consisting of three or more species frequently display chaotic dynamics which implies that long-term predictions of the population trajectories in time are impossible. Communities in the wild tend to be more complex, but evidence for chaotic dynamics from such communities is scarce. We used supercomputing power to test the hypothesis that chaotic dynamics become less frequent in model ecosystems when their complexity increases. We determined the dynamical stability of a universe of mathematical, nonlinear food web models with varying degrees of organizational complexity. We found that the frequency of unpredictable, chaotic dynamics increases with the number of trophic levels in a food web but decreases with the degree of complexity. Our results suggest that natural food webs possess architectural properties that may intrinsically lower the likelihood of chaotic community dynamics. [source] A comprehensive approach to characterization of the nonlinearity of runoff in the headwaters of the Tarim River, western ChinaHYDROLOGICAL PROCESSES, Issue 2 2010Jianhua Xu Abstract Nonlinear characteristics of the runoff processes in the headwaters of the Tarim River were identified and evaluated using several selected methods, including wavelet analysis, correlation dimension, and R/S analysis. Time-series of annual data describing runoff, average temperature, and precipitation from 1957 to 2005 were used to construct and test empirical models. The primary findings of this study were as follows: (1) The annual runoff of the headwaters are complex and nonlinear in nature, and they each presented periodic, nonlinear trends at the chosen time scales, chaotic dynamics, and long-memory characteristics. (2) These nonlinear trends appeared to have resulted from the regional climatic changes that occurred during the study period. The periodicity of changes in runoff occurred on an approximately 25-year cycle, which appeared to be correlated with temperature and precipitation cycles. In addition, the annual runoff exhibited a significant, positive correlation with the temperature and precipitation factors at the 4-, 8-, 16-, and 32-year temporal scales. (3) The correlation dimensions of the attractor derived from the runoff time series for the Hotan, Yarkand, and Aksu rivers were all greater than 3·0 and non-integral, implying that all three rivers are dynamic chaotic systems that are sensitive to initial conditions, and that the dynamic modelling of their annual runoff requires at least four independent variables. (4) The computed Hurst exponents indicate that a long-term memory characteristic exists in the annual runoff processes. However, there were some differences observed, with the Aksu and Yarkand rivers demonstrating a persistent trait, and the Hotan River exhibiting an anti-persistent feature. Copyright © 2009 John Wiley & Sons, Ltd. [source] Are weed population dynamics chaotic?JOURNAL OF APPLIED ECOLOGY, Issue 5 2002Robert P. Freckleton Summary 1There have been suggestions that the population dynamics of weeds may show chaotic dynamics, and that therefore it will not be possible to predict the impact of changing management regimes on weed abundance. The instability of weed populations is presumed to result either from overcompensating yield,density responses or from threshold management. 2Using theoretical arguments and empirical evidence we argue that this contention is likely to be incorrect. 3Overcompensating yield,density responses are unlikely in plant populations and this point has been extensively discussed. Such responses have only been observed in high-density artificially sown stands of weed populations. The form of chaos that results from threshold management is a consequence of high population growth resulting from the cessation of management when weed densities are lower than a threshold level. Consequently the dynamics of such populations may be argued to be extrinsically rather than intrinsically driven. 4There are many studies that have shown weed populations to be dynamically stable, both spatially and temporally. Here we present an analysis of data from the Broadbalk experiment that demonstrates long-term stability of 12 species of common weeds over a 12-year period. Using parameter estimates derived from the literature we show that the stability of these populations is similar to other annual species, both weedy and non-weedy. 5We argue that weed population dynamics are more generally better viewed as resulting from the impacts of broad-scale types of management, as well as temporal variability in population numbers. The significance of chaotic dynamics is likely to be minimal. [source] A Dependence Metric for Possibly Nonlinear ProcessesJOURNAL OF TIME SERIES ANALYSIS, Issue 5 2004C. W. Granger Abstract., A transformed metric entropy measure of dependence is studied which satisfies many desirable properties, including being a proper measure of distance. It is capable of good performance in identifying dependence even in possibly nonlinear time series, and is applicable for both continuous and discrete variables. A nonparametric kernel density implementation is considered here for many stylized models including linear and nonlinear MA, AR, GARCH, integrated series and chaotic dynamics. A related permutation test of independence is proposed and compared with several alternatives. [source] Photo-induced cytomorphologic changes in an advanced cancer phase I clinical trialLASERS IN SURGERY AND MEDICINE, Issue 1 2002Luis A. Santana-Blank MD Abstract Background and Objectives The aim of this study was to investigate whether the application of an Infrared Pulsed Laser Device (IPLD) photo-induced significant cytomorphologic changes during the monitoring of advanced cancer patients participating in a phase I clinical trial. Materials and Methods Patients were irradiated with an IPLD (904 nm pulsed at 3 MHz) under a one-dose, one-schedule, and one-procedure design. Total daily dose consisted of a Radiant Exposure of 4.5,×,105 J/m2. Thirty-one tissue samples from eleven patients with progressive solid neoplastic diseases (TNM IV, UICC) were obtained at three intervals: Time 0 (15,90 days pre-treatment, n,=,11); Time I (2,5 months post-treatment; n,=,11); Time II (6,12 months post-treatment, n,=,09). Three blinded pathologists evaluated samples; scores were determined by consensus. Data were evaluated by using the Wilcoxon matched-pairs signed-rank test and Spearman rank correlation coefficient. The level of statistical significance was ,,=,0.05. Results Increased apoptosis (Time I, P,<,0.003; Time II, P,<,0.007), necrosis (Time I, NS; Time II, P,<,0.01), cytoplasmic vacuoles (Time I, P,<,0.03; Time II, P,<,0.02), and nuclear vacuoles (Time I, NS; Time II, P,<,0.01), reduced cell size (Time I, P,<,0.007; Time II, P,<,0.01) and intercellular adhesion (Time I, P,<,0.01; Time II, P,<,0.02) were present in neoplastic cells after IPLD treatment. No apparent changes were noted in non-neoplastic cells. The Spearman rank correlation coefficient between apoptosis, necrosis, nuclear vacuoles, cytoplasmatic vacuoles, intercellular adhesion, and cell size was positive and highly significant (P,<,0.006). Conclusions Although further research is necessary, our preliminary results support the novel possibility that the IPLD photo-induces chaotic dynamics that modulate complex physiologically reparative bioeffects. Lasers Surg. Med. 30:18,25, 2002. © 2002 Wiley-Liss, Inc. [source] Long food chains are in general chaoticOIKOS, Issue 1 2005Thilo Gross The question whether chaos exists in nature is much debated. In this paper we prove that chaotic parameter regions exist generically in food chains of length greater than three. While nonchaotic dynamics is also possible, the presence of chaotic parameter regions indicates that chaotic dynamics is likely. We show that the chaotic regions survive even at high exponents of closure. Our results have been obtained using a general food chain model that describes a large class of different food chains. The existence of chaos in models of such generality can be deduced from the presence of certain bifurcations of higher codimension. [source] Identification of chaos in a regenerative cutting process by the 0-1 testPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009Grzegorz Litak We examine the regenerative cutting process by using a single degree of freedom non-smooth model with a friction component and a time delay term. Instead of the standard Lyapunov exponent calculations, we propose a statistical 0-1 test for chaos. This approach reveals the nature of the cutting process signaling regular or chaotic dynamics. We are able to show that regular or chaotic motion occur in the investigated model depending on the delay time. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A robust formulation of the ensemble Kalman filter,THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 639 2009S. J. Thomas Abstract The ensemble Kalman filter (EnKF) can be interpreted in the more general context of linear regression theory. The recursive filter equations are equivalent to the normal equations for a weighted least-squares estimate that minimizes a quadratic functional. Solving the normal equations is numerically unreliable and subject to large errors when the problem is ill-conditioned. A numerically reliable and efficient algorithm is presented, based on the minimization of an alternative functional. The method relies on orthogonal rotations, is highly parallel and does not ,square' matrices in order to compute the analysis update. Computation of eigenvalue and singular-value decompositions is not required. The algorithm is formulated to process observations serially or in batches and therefore easily handles spatially correlated observation errors. Numerical results are presented for existing algorithms with a hierarchy of models characterized by chaotic dynamics. Under a range of conditions, which may include model error and sampling error, the new algorithm achieves the same or lower mean square errors as the serial Potter and ensemble adjustment Kalman filter (EAKF) algorithms. Published in 2009 by John Wiley and Sons, Ltd. [source] | |||||||||||||