Multifractal Dimensional Dependence Assessment Based on Tsallis Mutual Information
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Complex systemGeneralized dimensionsMultifractalityNon-extensivitySeismicitySpace-time dynamicsTsallis entropy
Angulo Ibáñez, J.M.; Esquivel Sánchez, F.J. Multifractal Dimensional Dependence Assessment Based on Tsallis Mutual Information. Entropy, 17(8): 5382-5401 (2015). [http://hdl.handle.net/10481/38028]
SponsorshipThis work has been partially supported by the grant MTM2012-32666 of the Spanish Ministry of Economy and Competitiveness (co-financed by FEDER).
Entropy-based tools are commonly used to describe the dynamics of complex systems. In the last few decades, non-extensive statistics, based on Tsallis entropy, and multifractal techniques have shown to be useful to characterize long-range interaction and scaling behavior. In this paper, an approach based on generalized Tsallis dimensions is used for the formulation of mutual-information-related dependence coefficients in the multifractal domain. Different versions according to the normalizing factor, as well as to the inclusion of the non-extensivity correction term are considered and discussed. An application to the assessment of dimensional interaction in the structural dynamics of a seismic real series is carried out to illustrate the usefulness and comparative performance of the measures introduced.