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In this Letter, we show that coherence and phase synchronization analysis are sensitive but not specific in detecting the correct class of underlying dynamics. We propose procedures to increase specificity and demonstrate the power of the approach by application to paradigmatic dynamic model systems. (c) 2006 Elsevier B.V. All rights reserved
Spatial recurrence plots
(2006)
We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We show that the complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially coherent structures, such as synchronization domains, in lattice profiles. This approach has potential for many more applications, e.g., in surface roughness analyzes
The radiocarbon record that has been extended from 7199 BC to 1891 AD is of fundamental importance to understand century-scale variations of solar activity. We have, therefore, studied how to extract information from dynamic reconstructions of this observational record. Using some rather unusual methods of nonlinear dynamics, we have found that the data are significantly different from linear colored noise and that there is some evidence of nonlinear behavior. The method of recurrence plots exhibits that the grand minima of solar activity are quite different in their recurrence. Most remarkably, it suggests that the recent epoch seems to be similar to the Medieval maximum.
Many cellular processes require decision making mechanisms, which must act reliably even in the unavoidable presence of substantial amounts of noise. However, the multistable genetic switches that underlie most decision-making processes are dominated by fluctuations that can induce random jumps between alternative cellular states. Here we show, via theoretical modeling of a population of noise-driven bistable genetic switches, that reliable timing of decision-making processes can be accomplished for large enough population sizes, as long as cells are globally coupled by chemical means. In the light of these results, we conjecture that cell proliferation, in the presence of cell-cell communication, could provide a mechanism for reliable decision making in the presence of noise, by triggering cellular transitions only when the whole cell population reaches a certain size. In other words , the summation performed by the cell population would average out the noise and reduce its detrimental impact.
We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincaré map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincaré map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique.
The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances.
Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook