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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Analysis of Terrorism Data-series by means of Power Law and Pseudo Phase Plane

Discontinuity, Nonlinearity, and Complexity 4(4) (2015) 403--411 | DOI:10.5890/DNC.2015.11.004

António M. Lopes$^{1}$; J.A. Tenreiro Machado$^{2}$

1Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal

2Institute ofMechanical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

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Terrorist attacks are catastrophic events often accompanied by a large number of human losses. The statistics of these casualties can be approximated by Power Law (PL) distributions. In this paper we analyze a dataset of terrorist events by means of PL distributions and Pseudo Phase Plane (PPP) technique. We consider worldwide events grouped into 13 geographical regions. First, for each region, we approximate the empirical data by PL functions and we analyze the emerging PL parameters. Second, we model the dataset as time-series and interpret the data as the output of a dynamical system. For each region, we compute the correlation coefficient to find the optimal time delay for reconstructing the PPP. Third, we compare the PPP curves using clustering tools in order to unveil relationships among the data.


National Consortium for the Study of Terrorism and Responses to Terrorism (START). (2013). Global Terrorism Database [Data file]. Retrieved from


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