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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


Fractional Fourier Detection of Lévy Flights Application to Hamiltonian Chaotic Trajectories

Discontinuity, Nonlinearity, and Complexity 2(2) (2013) 103--114 | DOI:10.5890/DNC.2013.04.001

Françoise Briolle$^{1}$,$^{2}$; Xavier Leoncini$^{2}$; Benjamin Ricaud$^{3}$

$^{1}$ CReA, BA 701 Salon de Provence 13300, France

$^{2}$ Centre de Physique Théorique, CNRS-Aix-Marseille Université, Campus de Luminy, Case 907, F-13288 Marseille cedex 9, France

$^{3}$ Institute of Electrical Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

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A signal processing method designed for the detection of linear (coherent) behaviors among random fluctuations is presented. It is dedicated to the study of data recorded from nonlinear physical systems. More precisely the method is suited for signals having chaotic variations and sporadically regular linear patterns, possibly impaired by noise. We use time-frequency techniques and the Fractional Fourier transform in order to make it robust and easily implementable. The method is illustrated with an example of application: the analysis of chaotic trajectories of advected passive particles. The signal has a chaotic behavior and encounters Lévy flights (straight lines). The method allows to detect and quantify these ballistic transport regions, even in noisy situations.


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