Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic R\"ossler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.Comment: 12 pages, 13 figure

Effects of non-denumerable fixed points in finite dynamical systems

The motion of a spinning football brings forth the possible existence of a whole class of finite dynamical systems where there may be non-denumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point that a point on the fixed point in the phase space should remain there forever, for, a fixed point can evolve as well! Under such considerations one can argue that a free-kicked football should be non-chaotic.Comment: This paper is a replaced version to modify the not-so-true claim, made unknowingly in the earlier version, of being first to propose the peculiar dynamical systems as described in the paper. With respect to the original workers, we present here our original finding

Persistent Chaos in High Dimensions

An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter windows with periodic behavior decreases. A subset of parameter space remains in which topological change induced by small parameter variation is very common. It turns out, however, that if the system's dimension is sufficiently high, this inevitable, and expected, topological change is never catastrophic, in the sense chaotic behavior is preserved. One concludes that deterministic chaos is persistent in high dimensions.Comment: 4 pages, 3 figures; Changes in response to referee comment

Structures of minor ether lipids isolated from the aceticlastic methanogen, Methanothrix concilii GP6.

Structures were determined for two phospholipids and three glycolipids purified from chloroform-methanol extracts of Methanothrix concilii GP6. Together they accounted for 14% of the total lipid and were based on a C20,20-diether core structure consisting of either 2,3-di-O-phytanyl-sn-glycerol or its 3'-hydroxy analog, namely, 2-O-[3,7,11,15-tetramethylhexadecyl]-3-O-[3'- hydroxy-3',7',11',15'-tetramethylhexadecyl]-sn-glycerol. These two core lipids formed phosphodiester bonds to ethanolamine and glycosidic bonds to beta-D-galactopyranose. A third glycolipid consisted of the triglycosyl head group beta-D-galactopyranosyl-(1----6)-[beta-D-glucopyranosyl-(1----3)]-beta-D - galactopyranose in glycosidic linkage to the 3'-hydroxydiether core lipid

A Model for Estimating Demand for Irrigation Water on the Texas High Plains

With rapidly changing conditions in production agriculture, the need for highly flexible and quickly applicable methods of analysis is emphasized. The purpose of this study was to develop such a model for a homogeneous production region in the Texas High Plains. A linear programming model was constructed whereby crop or input prices are readily adjustable. In addition, limitations on quantities of inputs available can easily be evaluated. The model contains cotton, grain sorghum, corn, wheat and soybeans. Inputs that can be evaluated include irrigation water, natural gas, diesel, nitrogen fertilizer and herbicides. The primary focus of this work was to estimate the demand for irrigation water in the study area. The model was applied using alternative crop prices and input prices. Assuming average crop prices, current input prices and only variable costs of production, as the price of water was increased wheat shifted from irrigated to dryland production, then grain sorghum, cotton, corn and soybeans, in that order. The price of water was $71.75 per acre foot plus current pumping cost when all land shifted to dryland production. The same analysis, except variable and fixed costs both included, gave similar results relative to the sequence of crops that shift to dryland production as the price of water was increased. However, the shifts occurred at much lower water prices; i.e., at$24.47 per acre foot plus current pumping costs, all land had shifted to dryland production. This suggests that over the long run, irrigation in the Texas High Plains is quite sensitive to the price of energy used in pumping water. Further, there are strong implications relative to farmer's "ability to pay" for water imported to the High Plains from other regions. In this report, several scenarios including low, high and average crop prices and average and high input prices were evaluated

Boundary condition independence of molecular dynamics simulations of planar elongational flow

The simulation of liquid systems in a nonequilibrium steady state under planar elongational flow (PEF) for indefinite time is possible only with the use of the so-called Kraynik-Reinelt (KR) periodic boundary conditions (PBCs) on the simulation cell. These conditions admit a vast range of implementation parameters, which regulate how the unit lattice is deformed under elongation and periodically remapped onto itself. Clearly, nonequilibrium properties of homogeneous systems in a steady state have to be independent of the boundary conditions imposed on the unit cell. In order to confirm the independence of measurable properties of a system under PEF from the particular set of periodic boundary conditions, we compute the Lyapunov spectra, apply the conjugate pairing rule, and carefully analyze the so-called unpaired exponents for an atomic fluid of various sizes and state points. We further compute the elongational viscosity for various implementations of boundary conditions. All our results confirm the independence from KR PBCs for the dynamics of phase-space trajectories and for the transport coefficients

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure

Prospective Epidemiological Observations on the Course of the Disease in Fibromyalgia Patients

OBJECTIVES: The aim of the study was to carry out a survey in patients with fibromyalgia (FM), to examine their general health status and work incapacity (disability-pension status), and their views on the effectiveness of therapy received, over a two-year observation period. METHODS: 48 patients diagnosed with FM, according to the American College of Rheumatology (ACR) criteria, took part in the study. At baseline, and on average two years later, the patients underwent clinical investigation (dolorimetry, laboratory diagnostics, medical history taking) and completed the Fibromyalgia questionnaire (Dettmer and Chrostek [1]). RESULTS: 27/48 (56%) patients participated in the two-year follow-up. In general, the patients showed no improvement in their symptoms over the observation period, regardless of the type of therapy they had received. General satisfaction with quality of life improved, as did satisfaction regarding health status and the family situation, although the degree of pain experienced remain unchanged. In comparison with the initial examination, there was no change in either work-capacity or disability-pension status. CONCLUSIONS: The FM patients showed no improvement in pain, despite the many various treatments received over the two-year period. The increase in general satisfaction over the observation period was believed to be the result of patient instruction and education about the disease. To what extent a population of patients with FM would show similar outcomes if they did not receive any instruction/education about their disorder, cannot be ascertained from the present study; and, indeed, the undertaking of a study to investigate this would be ethically questionable. As present, no conclusions can be made regarding the influence of therapy on the primary and secondary costs associated with FM

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identifiy the irreversible nature of the series.Comment: submitted for publicatio