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- 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.
- ItemExperimental Study of the Triplet Synchronization of Coupled Nonidentical Mechanical Metronomes(London : Nature Publishing Group, 2015) Jia, J.; Song, Z.; Liu, W.; Kurths, J.; Xiao, J.
- 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.
- ItemBasin stability in delayed dynamics(London : Nature Publishing Group, 2016) Leng, S.; Lin, W.; Kurths, J.
- ItemSynchronization in output-coupled temporal Boolean networks(London : Nature Publishing Group, 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.
- ItemCorrelating the ancient Maya and modern european calendars with high-precision AMS 14C dating(London : Nature Publishing Group, 2013) Kennett, D.J.; Hajdas, I.; Culleton, B.J.; Belmecheri, S.; Martin, S.; Neff, H.; Awe, J.; Graham, H.V.; Freeman, K.H.; Newsom, L.; Lentz, D.L.; Anselmetti, F.S.; Robinson, M.; Marwan, N.; Southon, J.; Hodell, D.A.; Haug, G.H.The reasons for the development and collapse of Maya civilization remain controversial and historical events carved on stone monuments throughout this region provide a remarkable source of data about the rise and fall of these complex polities. Use of these records depends on correlating the Maya and European calendars so that they can be compared with climate and environmental datasets. Correlation constants can vary up to 1000 years and remain controversial.Wereport a series of high-resolution AMS14C dates on a wooden lintel collected from the Classic Period city of Tikal bearing Maya calendar dates. The radiocarbon dates were calibrated using a Bayesian statistical model and indicate that the dates were carved on the lintel betweenAD 658-696. This strongly supports the Goodman-Mart?nez-Thompson (GMT) correlation and the hypothesis that climate change played an important role in the development and demise of this complex civilization.
- ItemRobustness of interrelated traffic networks to cascading failures(London : Nature Publishing Group, 2014) Su, Z.; Li, L.; Peng, H.; Kurths, J.; Xiao, J.; Yang, Y.The vulnerability to real-life networks against small initial attacks has been one of outstanding challenges in the study of interrelated networks. We study cascading failures in two interrelated networks S and B composed from dependency chains and connectivity links respectively. This work proposes a realistic model for cascading failures based on the redistribution of traffic flow. We study the Barabási-Albert networks (BA) and Erd's-Rényi graphs (ER) with such structure, and found that the efficiency sharply decreases with increasing percentages of the dependency nodes for removing a node randomly. Furthermore, we study the robustness of interrelated traffic networks, especially the subway and bus network in Beijing. By analyzing different attacking strategies, we uncover that the efficiency of the city traffic system has a non-equilibrium phase transition at low capacity of the networks. This explains why the pressure of the traffic overload is relaxed by singly increasing the number of small buses during rush hours. We also found that the increment of some buses may release traffic jam caused by removing a node of the bus network randomly if the damage is limited. However, the efficiencies to transfer people flow will sharper increase when the capacity of the subway network αS > α0.
- ItemThe Dynamics of Coalition Formation on Complex Networks(London : Nature Publishing Group, 2015) Auer, Sören; Heitzig, J.; Kornek, U.; Schöll, E.; Kurths, J.
- ItemLow-dimensional behavior of Kuramoto model with inertia in complex networks(London : Nature Publishing Group, 2014) Ji, P.; Peron, T.K.D.M.; Rodrigues, F.A.; Kurths, J.Low-dimensional behavior of large systems of globally coupled oscillators has been intensively investigated since the introduction of the Ott-Antonsen ansatz. In this report, we generalize the Ott-Antonsen ansatz to second-order Kuramoto models in complex networks. With an additional inertia term, we find a low-dimensional behavior similar to the first-order Kuramoto model, derive a self-consistent equation and seek the time-dependent derivation of the order parameter. Numerical simulations are also conducted to verify our analytical results.
- ItemNetworks from Flows - From Dynamics to Topology(London : Nature Publishing Group, 2014) Molkenthin, N.; Rehfeld, K.; Marwan, N.; Kurths, J.Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure. However the relationship between the underlying atmospheric or oceanic flow's dynamics and the estimated network measures have remained largely unclear. We bridge this crucial gap in a bottom-up approach and define a continuous analytical analogue of Pearson correlation networks for advection-diffusion dynamics on a background flow. Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks. The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness mark transition zones in the flow rather than, as previously thought, the propagation of dynamical information.