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Fractional State Space Analysis of Economic Systems

Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal
Nova SBE, Universidade Nova de Lisboa, Faculdade de Economia, Campus de Campolide, Lisbon, Portugal
UISPA-LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Kevin H. Knuth
Entropy 2015, 17(8), 5402-5421;
Received: 15 June 2015 / Revised: 16 July 2015 / Accepted: 27 July 2015 / Published: 29 July 2015
(This article belongs to the Special Issue Complex and Fractional Dynamics)
PDF [2847 KB, uploaded 29 July 2015]


This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis. View Full-Text
Keywords: state space portrait; fractional calculus; multidimensional scaling; economic growth; convergence and divergence; colonizers and offshores state space portrait; fractional calculus; multidimensional scaling; economic growth; convergence and divergence; colonizers and offshores

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Machado, J.A.T.; Mata, M.E.; Lopes, A.M. Fractional State Space Analysis of Economic Systems. Entropy 2015, 17, 5402-5421.

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