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We present two different approaches to detect and quantify phase synchronization in the case of coupled non- phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the Rossler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators
Phase models are a powerful method to quantify the coupled dynamics of nonlinear oscillators from measured data. We use two phase modeling methods to quantify the dynamics of pairs of coupled electrochemical oscillators, based on the phases of the two oscillators independently and the phase difference, respectively. We discuss the benefits of the two-dimensional approach relative to the one-dimensional approach using phase difference. We quantify the dependence of the coupling functions on the coupling magnitude and coupling time delay. We show differences in synchronization predictions of the two models using a toy model. We show that the two-dimensional approach reveals behavior not detected by the one-dimensional model in a driven experimental oscillator. This approach is broadly applicable to quantify interactions between nonlinear oscillators, especially where intrinsic oscillator sensitivity and coupling evolve with time.
River ecosystems receive and process vast quantities of terrestrial organic carbon, the fate of which depends strongly on microbial activity. Variation in and controls of processing rates, however, are poorly characterized at the global scale. In response, we used a peer-sourced research network and a highly standardized carbon processing assay to conduct a global-scale field experiment in greater than 1000 river and riparian sites. We found that Earth’s biomes have distinct carbon processing signatures. Slow processing is evident across latitudes, whereas rapid rates are restricted to lower latitudes. Both the mean rate and variability decline with latitude, suggesting temperature constraints toward the poles and greater roles for other environmental drivers (e.g., nutrient loading) toward the equator. These results and data set the stage for unprecedented “next-generation biomonitoring” by establishing baselines to help quantify environmental impacts to the functioning of ecosystems at a global scale.