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When optimization for governing human-environment tipping elements is neither sustainable nor safe

2018, Barfuss, W., Donges, J.F., Lade, S.J., Kurths, J.

Optimizing economic welfare in environmental governance has been criticized for delivering short-term gains at the expense of long-term environmental degradation. Different from economic optimization, the concepts of sustainability and the more recent safe operating space have been used to derive policies in environmental governance. However, a formal comparison between these three policy paradigms is still missing, leaving policy makers uncertain which paradigm to apply. Here, we develop a better understanding of their interrelationships, using a stylized model of human-environment tipping elements. We find that no paradigm guarantees fulfilling requirements imposed by another paradigm and derive simple heuristics for the conditions under which these trade-offs occur. We show that the absence of such a master paradigm is of special relevance for governing real-world tipping systems such as climate, fisheries, and farming, which may reside in a parameter regime where economic optimization is neither sustainable nor safe.

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Sample-based approach can outperform the classical dynamical analysis - Experimental confirmation of the basin stability method

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.

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Experimental Study of the Triplet Synchronization of Coupled Nonidentical Mechanical Metronomes

2015, Jia, J., Song, Z., Liu, W., Kurths, J., Xiao, J.

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Synchronization in output-coupled temporal Boolean networks

2014, Lu, J., Zhong, J., Tang, Y., Huang, T., Cao, J., Kurths, J.

This paper presents an analytical study of synchronization in an array of output-coupled temporal Boolean networks. A temporal Boolean network (TBN) is a logical dynamic system developed to model Boolean networks with regulatory delays. Both state delay and output delay are considered, and these two delays are assumed to be different. By referring to the algebraic representations of logical dynamics and using the semi-tensor product of matrices, the output-coupled TBNs are firstly converted into a discrete-time algebraic evolution system, and then the relationship between the states of coupled TBNs and the initial state sequence is obtained. Then, some necessary and sufficient conditions are derived for the synchronization of an array of TBNs with an arbitrary given initial state sequence. Two numerical examples including one epigenetic model are finally given to illustrate the obtained results.

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Metastability for discontinuous dynamical systems under Lévy noise: Case study on Amazonian Vegetation

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.

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A regime shift in the Sun-Climate connection with the end of the Medieval Climate Anomaly

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.

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Reconstruction of Complex Network based on the Noise via QR Decomposition and Compressed Sensing

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.

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Restoration of rhythmicity in diffusively coupled dynamical networks

2015, Zou, W., Senthilkumar, D.V., Nagao, R., Kiss, I.Z., Tang, Y., Koseska, A., Duan, J., Kurths, J.

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The Switch in a Genetic Toggle System with Lévy Noise

2016, Xu, Y., Li, Y., Zhang, H., Li, X., Kurths, J.

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Basin stability in delayed dynamics

2016, Leng, S., Lin, W., Kurths, J.