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Author: Kurths, J. × Type: Text × Publisher: London : Nature Publishing Group × Subject: noise ×

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Now showing 1 - 3 of 3
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    Metastability 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.
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    The Switch in a Genetic Toggle System with Lévy Noise
    (London : Nature Publishing Group, 2016) Xu, Y.; Li, Y.; Zhang, H.; Li, X.; Kurths, J.
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    Reconstruction 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.