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The Persistence of Memory

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Abstract

This paper analyzes several natural and man-made complex phenomena in the perspective of dynamical systems. Such phenomena are often characterized by the absence of a characteristic length-scale, long range correlations and persistent memory, which are features also associated to fractional order systems. For each system, the output, interpreted as a manifestation of the system dynamics, is analyzed by means of the Fourier transform. The amplitude spectrum is approximated by a power law function and the parameters are interpreted as an underlying signature of the system dynamics. The complex systems under analysis are then compared in a global perspective in order to unveil and visualize hidden relationships among them.

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Acknowledgments

The authors acknowledge the inspiration of the paintings ‘The Persistence of Memory’ (http://en.wikipedia.org/wiki/The_Persistence_of_Memory) and ‘The Disintegration of the Persistence of Memory’ (http://en.wikipedia.org/wiki/The_Disintegration_of_the_Persistence_of_Memory), by Salvador Dali (http://en.wikipedia.org/wiki/Salvador_Dal%C3%AD).

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Authors and Affiliations

  1. Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072, Porto, Portugal

    J. A. Tenreiro Machado

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

    António M. Lopes

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Tenreiro Machado, J.A., Lopes, A.M. The Persistence of Memory. Nonlinear Dyn 79, 63–82 (2015). https://doi.org/10.1007/s11071-014-1645-1

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