7 results
Search Results
Now showing 1 - 7 of 7
- ItemSample-based approach can outperform the classical dynamical analysis - Experimental confirmation of the basin stability method(London : Nature Publishing Group, 2017) Brzeski, P.; Wojewoda, J.; Kapitaniak, T.; Kurths, J.; Perlikowski, P.In this paper we show the first broad experimental confirmation of the basin stability approach. The basin stability is one of the sample-based approach methods for analysis of the complex, multidimensional dynamical systems. We show that investigated method is a reliable tool for the analysis of dynamical systems and we prove that it has a significant advantages which make it appropriate for many applications in which classical analysis methods are difficult to apply. We study theoretically and experimentally the dynamics of a forced double pendulum. We examine the ranges of stability for nine different solutions of the system in a two parameter space, namely the amplitude and the frequency of excitation. We apply the path-following and the extended basin stability methods (Brzeski et al., Meccanica 51(11), 2016) and we verify obtained theoretical results in experimental investigations. Comparison of the presented results show that the sample-based approach offers comparable precision to the classical method of analysis. However, it is much simpler to apply and can be used despite the type of dynamical system and its dimensions. Moreover, the sample-based approach has some unique advantages and can be applied without the precise knowledge of parameter values.
- ItemA regime shift in the Sun-Climate connection with the end of the Medieval Climate Anomaly(London : Nature Publishing Group, 2017) Smirnov, D.A.; Breitenbach, S.F.M.; Feulner, G.; Lechleitner, F.A.; Prufer, K.M.; Baldini, J.U.L.; Marwan, N.; Kurths, J.Understanding the influence of changes in solar activity on Earth's climate and distinguishing it from other forcings, such as volcanic activity, remains a major challenge for palaeoclimatology. This problem is best approached by investigating how these variables influenced past climate conditions as recorded in high precision paleoclimate archives. In particular, determining if the climate system response to these forcings changes through time is critical. Here we use the Wiener-Granger causality approach along with well-established cross-correlation analysis to investigate the causal relationship between solar activity, volcanic forcing, and climate as reflected in well-established Intertropical Convergence Zone (ITCZ) rainfall proxy records from Yok Balum Cave, southern Belize. Our analysis reveals a consistent influence of volcanic activity on regional Central American climate over the last two millennia. However, the coupling between solar variability and local climate varied with time, with a regime shift around 1000-1300 CE after which the solar-climate coupling weakened considerably.
- ItemMetastability for discontinuous dynamical systems under Lévy noise: Case study on Amazonian Vegetation(London : Nature Publishing Group, 2017) Serdukova, L.; Zheng, Y.; Duan, J.; Kurths, J.For the tipping elements in the Earth's climate system, the most important issue to address is how stable is the desirable state against random perturbations. Extreme biotic and climatic events pose severe hazards to tropical rainforests. Their local effects are extremely stochastic and difficult to measure. Moreover, the direction and intensity of the response of forest trees to such perturbations are unknown, especially given the lack of efficient dynamical vegetation models to evaluate forest tree cover changes over time. In this study, we consider randomness in the mathematical modelling of forest trees by incorporating uncertainty through a stochastic differential equation. According to field-based evidence, the interactions between fires and droughts are a more direct mechanism that may describe sudden forest degradation in the south-eastern Amazon. In modeling the Amazonian vegetation system, we include symmetric α-stable Lévy perturbations. We report results of stability analysis of the metastable fertile forest state. We conclude that even a very slight threat to the forest state stability represents Ĺevy noise with large jumps of low intensity, that can be interpreted as a fire occurring in a non-drought year. During years of severe drought, high-intensity fires significantly accelerate the transition between a forest and savanna state.
- ItemExperimental investigation on preconditioned rate induced tipping in a thermoacoustic system(London : Nature Publishing Group, 2017) Tony, J.; Subarna, S.; Syamkumar, K.S.; Sudha, G.; Akshay, S.; Gopalakrishnan, E.A.; Surovyatkina, E.; Sujith, R.I.Many systems found in nature are susceptible to tipping, where they can shift from one stable dynamical state to another. This shift in dynamics can be unfavorable in systems found in various fields ranging from ecology to finance. Hence, it is important to identify the factors that can lead to tipping in a physical system. Tipping can mainly be brought about by a change in parameter or due to the influence of external fluctuations. Further, the rate at which the parameter is varied also determines the final state that the system attains. Here, we show preconditioned rate induced tipping in experiments and in a theoretical model of a thermoacoustic system. We provide a specific initial condition (preconditioning) and vary the parameter at a rate higher than a critical rate to observe tipping. We find that the critical rate is a function of the initial condition. Our study is highly relevant because the parameters that dictate the asymptotic behavior of many physical systems are temporally dynamic.
- ItemThe role of city size and urban form in the surface urban heat island(London : Nature Publishing Group, 2017) Zhou, B.; Rybski, D.; Kropp, J.P.Urban climate is determined by a variety of factors, whose knowledge can help to attenuate heat stress in the context of ongoing urbanization and climate change. We study the influence of city size and urban form on the Urban Heat Island (UHI) phenomenon in Europe and find a complex interplay between UHI intensity and city size, fractality, and anisometry. Due to correlations among these urban factors, interactions in the multi-linear regression need to be taken into account. We find that among the largest 5,000 cities, the UHI intensity increases with the logarithm of the city size and with the fractal dimension, but decreases with the logarithm of the anisometry. Typically, the size has the strongest influence, followed by the compactness, and the smallest is the influence of the degree to which the cities stretch. Accordingly, from the point of view of UHI alleviation, small, disperse, and stretched cities are preferable. However, such recommendations need to be balanced against e.g. positive agglomeration effects of large cities. Therefore, trade-offs must be made regarding local and global aims.
- ItemReconstruction of Complex Network based on the Noise via QR Decomposition and Compressed Sensing(London : Nature Publishing Group, 2017) Li, L.; Xu, D.; Peng, H.; Kurths, J.; Yang, Y.It is generally known that the states of network nodes are stable and have strong correlations in a linear network system. We find that without the control input, the method of compressed sensing can not succeed in reconstructing complex networks in which the states of nodes are generated through the linear network system. However, noise can drive the dynamics between nodes to break the stability of the system state. Therefore, a new method integrating QR decomposition and compressed sensing is proposed to solve the reconstruction problem of complex networks under the assistance of the input noise. The state matrix of the system is decomposed by QR decomposition. We construct the measurement matrix with the aid of Gaussian noise so that the sparse input matrix can be reconstructed by compressed sensing. We also discover that noise can build a bridge between the dynamics and the topological structure. Experiments are presented to show that the proposed method is more accurate and more efficient to reconstruct four model networks and six real networks by the comparisons between the proposed method and only compressed sensing. In addition, the proposed method can reconstruct not only the sparse complex networks, but also the dense complex networks.
- ItemReducing Urban Greenhouse Gas Footprints(London : Nature Publishing Group, 2017) Pichler, P.-P.; Zwickel, T.; Chavez, A.; Kretschmer, T.; Seddon, J.; Weisz, H.Cities are economically open systems that depend on goods and services imported from national and global markets to satisfy their material and energy requirements. Greenhouse Gas (GHG) footprints are thus a highly relevant metric for urban climate change mitigation since they not only include direct emissions from urban consumption activities, but also upstream emissions, i.e. emissions that occur along the global production chain of the goods and services purchased by local consumers. This complementary approach to territorially-focused emission accounting has added critical nuance to the debate on climate change mitigation by highlighting the responsibility of consumers in a globalized economy. Yet, city officials are largely either unaware of their upstream emissions or doubtful about their ability to count and control them. This study provides the first internationally comparable GHG footprints for four cities (Berlin, Delhi NCT, Mexico City, and New York metropolitan area) applying a consistent method that can be extended to other global cities using available data. We show that upstream emissions from urban household consumption are in the same order of magnitude as cities' overall territorial emissions and that local policy leverage to reduce upstream emissions is larger than typically assumed.