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Author: Kurths, Jürgen × End date: 2023 × Type: Text × Type: article ×

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Now showing 1 - 3 of 3
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    Emotional tendencies in online social networking: a statistical analysis
    (London : Taylor & Francis Open, 2016) Zhang, Xianhan; Zhang, Nan; Zhao, Letong; Zhang, Ruihan; Cao, Jinde; Lu, Jianquan; Kurths, Jürgen; Qian, Cheng
    Numerous previous studies suggested that people's emotional tendency (ET) towards an issue can often be affected by others. But in some cases, people are unwilling to believe opposite points. This paper aims to study whether people's emotional tendencies (ET) are susceptible with exposures to others' ET concerning a special topic. ET contained in 798,057 pieces of private-information-deleted Chinese Weibo posts are carefully investigated via a revised genetic algorithm, a nonlinear method. Note that nearly all of the posts are closely related to a special topic, the terrible earthquake happen in Japan, 11 March 2011. By conducting statistical analysis including coefficient calculations and hypothesis testing, this study shows that concerning this particular topic, Chinese citizens' first impressions about Japan are solid enough to form their ET and would not be easily altered. Moreover, according to analysis and discussion, we discover that node-to-node impact is exaggerated in some theoretical information diffusion models. Instead it is actually the interaction between nodes' properties and the spread information that matters in the process of information diffusions.
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    Survivability of deterministic dynamical systems
    (London : Nature Publishing Group, 2016) Hellmann, Frank; Schultz, Paul; Grabow, Carsten; Heitzig, Jobst; Kurths, Jürgen
    The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures.
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    Path integral solutions for n-dimensional stochastic differential equations under α-stable Lévy excitation
    (College Park, Md : [Verlag nicht ermittelbar], 2023) Zan, Wanrong; Xu, Yong; Kurths, Jürgen
    In this paper, the path integral solutions for a general n-dimensional stochastic differential equations (SDEs) with α-stable Lévy noise are derived and verified. Firstly, the governing equations for the solutions of n-dimensional SDEs under the excitation of α-stable Lévy noise are obtained through the characteristic function of stochastic processes. Then, the short-time transition probability density function of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski (CKS) equation and the characteristic function, and its correctness is demonstrated by proving that it satisfies the governing equation of the solution of the SDE, which is also called the Fokker-Planck-Kolmogorov equation. Besides, illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method, and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.