Desynchronization of systems of coupled Hindmarsh-Rose oscillators

It is widely assumed that neural activity related to synchronous rhythms of large portions of neurons in specific locations of the brain is responsible for the pathology manifested in patients' uncontrolled tremor and other similar diseases. To model such systems Hindmarsh-Rose (HR) oscillators are considered as appropriate as they mimic the qualitative behaviour of neuronal firing. Here we consider a large number of identical HR-oscillators interacting through the mean field created by the corresponding components of all oscillators. Introducing additional coupling by feedback of Pyragas type, proportional to the difference between the current value of the mean-field and its value some time in the past, Rosenblum and Pikovsky (Phys. Rev. E 70, 041904, 2004) demonstrated that the desirable desynchronization could be achieved with appropriate set of parameters for the system. Following our experience with stabilization of unstable steady states in dynamical systems, we show that by introducing a variable delay, desynchronization is obtainable for much wider range of parameters and that at the same time it becomes more pronounced.Comment: 5 pages, 2 figures, RevTe

Experimental time-delayed feedback control with variable and distributed delays

We report on several improvements of the classical time-delayed feedback control method for stabilization of unstable periodic orbits or steady states. In an electronic circuit experiment, we were able to realize time-varying and distributed delays in the control force leading to successful control for large parameter sets, including large time delays. The presented techniques make advanced use of the natural torsion of the orbits, which is also necessary for the original control method to work. ©2012 American Physical SocietyPeer reviewe

Delayed feedback control of unstable steady states with high-frequency modulation of the delay

We analyze the stabilization of unstable steady states by delayed feedback control with a periodic time-varying delay in the regime of a high-frequency modulation of the delay. The average effect of the delayed feedback term in the control force is equivalent to a distributed delay in the interval of the modulation, and the obtained distribution depends on the type of the modulation. In our analysis we use a simple generic normal form of an unstable focus, and investigate the effects of phase-dependent coupling and the influence of the control loop latency on the controllability. In addition, we have explored the influence of the modulation of the delays in multiple delay feedback schemes consisting of two independent delay lines of Pyragas type. A main advantage of the variable delay is the considerably larger domain of stabilization in parameter space. © 2013 American Physical Society.This work was supported by Deutsche Forschungsgemeinschaft in the framework of SFB 910: “Control of self-organizing nonlinear systems: Theoretical methods and concepts of application”. T.J. acknowledges support by FEDER (EU) under the project FISICOS (FIS2007-60327).Peer Reviewe

First thorough identification of factors associated with Cd, Hg and Pb concentrations in mosses sampled in the European Surveys 1990, 1995, 2000 and 2005

The aim of this study was, for the first time ever, to thoroughly identify the factors influencing Cd, Hg and Pb concentrations in mosses sampled within the framework of the European Heavy Metals in Mosses Surveys 1990–2005. These investigations can be seen as a follow up of a previous study where only the moss data recorded in the survey 2005 was included in the analysis (Schröder et al. 2010). The analyses of this investigation give a complete overview on the statistical association of Cd, Hg and Pb concentrations in mosses and sampling site-specific and regional characteristics, encompassing data from 4661 (1990), 7301 (1995), 6764 (2000) and 5600 (2005) sampling sites across Europe. From the many metals monitored in the European moss surveys, Cd, Hg and Pb were used as examples, since only for these three metals deposition measurements are being recorded in the framework of the European Monitoring and Evaluation Programme (EMEP). As exemplary case studies revealed that other factors besides atmospheric deposition of metals influence the element concentrations in mosses, the moss datasets of the above mentioned surveys were analysed by means of bivariate statistics and decision tree analysis in order to identify factors influencing metal bioaccumulation. In the analyses we used the metadata recorded during the sampling as well as additional geodata on, e.g., depositions, emissions and land use. Bivariate Spearman correlation analyses showed the highest correlations between Cd and Pb concentrations in mosses and EMEP modelled total deposition data (0.62 ≤ rs ≤ 0.73). For Hg the correlations with all the tested factors were considerably lower (e.g. total deposition r s  ≤ 0.24). Decision tree analyses by means of Classification and Regression Trees (CART) identified the total deposition as the statistically most significant factor for the Cd and Pb concentrations in the mosses in all four monitoring campaigns. For Hg, the most significant factor in 1990 as identified by CART was the distance to the nearest Hg source recorded in the European Pollutant Emission Register, in 1995 and 2000 it was the analytical method, and in 2005 it was the sampled moss species. The strong correlations between the Cd and Pb concentrations in the mosses and the total deposition can be used to calculate deposition maps with a regression kriging approach on the basis of surface maps on the element concentrations in the mosse

Are cadmium, lead and mercury concentrations in mosses across Europe primarily determined by atmospheric deposition of these metals?

Purpose This study aimed at investigating correlations between heavy metal concentrations in mosses and modelled deposition values as well as other site-specific and regional characteristics to determine which factors primarily affect cadmium, lead and mercury concentrations in mosses. The resulting relationships could potentially be used to enhance the spatial resolution of heavy metal deposition maps across Europe. Materials and methods Modelled heavy metal deposition data and data on the concentration of heavy metals in naturally growing mosses were integrated into a geographic information system and analysed by means of bivariate rank correlation analysis and multivariate decision trees. Modelled deposition data were validated annually with deposition measurements at up to 63 EMEP measurement stations within the European Monitoring and Evaluation Programme (EMEP), and mosses were collected at up to 7,000 sites at 5- year intervals between 1990 and 2005. Results and discussion Moderate to high correlations were found between cadmium and lead concentrations in mosses and modelled atmospheric deposition of these metals: Spearman rank correlation coefficients were between 0.62 and 0.67, and 0.67 and 0.73 for cadmium and lead, respectively (p<0.001). Multivariate decision tree analyses showed that cadmium and lead concentrations in mosses were primarily determined by the atmospheric deposition of these metals, followed by emissions of the metals. Low to very low correlations were observed between mercury concentrations in mosses and modelled atmospheric deposition of mercury. According to the multivariate analyses, spatial variations of the mercury concentration in mosses was primarily associated with the sampled moss species and not with the modelled deposition, but regional differences in the atmospheric chemistry of mercury and corresponding interactions with the moss may also be involved. Conclusions At least for cadmium and lead, concentrations in mosses are a valuable tool in determining and mapping the spatial variation in atmospheric deposition across Europe at a high spatial resolution. For mercury, more studies are needed to elucidate interactions of different chemical species with the moss