Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

Machado, J. A. Tenreiro; Lopes, António M.

doi:10.1515/fca-2015-0029

Cited by 47 publications

(16 citation statements)

References 48 publications

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“…The FC generalizes the derivative of a function f , D α f (x), to orders α ∈ R [27,28]. During the last decades FC has become a popular tool [29][30][31], and new areas of application have emerged. The modeling finance [32] and economy [18,21,22,26,[33][34][35] phenomena became of particular relevance.…”

Section: The Fractional Calculusmentioning

confidence: 99%

Fractional Dynamics and Pseudo-Phase Space of Country Economic Processes

2020

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In this paper, the fractional calculus (FC) and pseudo-phase space (PPS) techniques are combined for modeling the dynamics of world economies, leading to a new approach for forecasting a country’s gross domestic product. In most market economies, the decline of the post-war prosperity brought challenging rivalries to the Western world. Considerable social, political, and military unrest is today spreading in major capital cities of the world. As global troubles including mass migrations and more abound, countries’ performance as told by PPS approaches can help to assess national ambitions, commercial aggression, or hegemony in the current global environment. The 1973 oil shock was the turning point for a long-run crisis. A PPS approach to the last five decades (1970–2018) demonstrates that convergence has been the rule. In a sample of 15 countries, Turkey, Russia, Mexico, Brazil, Korea, and South Africa are catching-up to the US, Canada, Japan, Australia, Germany, UK, and France, showing similarity in many respects with these most developed countries. A substitution of the US role as great power in favor of China may still be avoided in the next decades, while India remains in the tail. The embedding of the two mathematical techniques allows a deeper understanding of the fractional dynamics exhibited by the world economies. Additionally, as a byproduct we obtain a foreseeing technique for estimating the future evolution based on the memory of the time series.

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Section: The Fractional Calculusmentioning

confidence: 99%

Fractional Dynamics and Pseudo-Phase Space of Country Economic Processes

2020

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“…FC emerged as a key tool in the area of dynamical systems with complex behavior and non-locality. Nowadays, the FC concepts are applied in different scientific fields, namely mathematics, physics, biology, finance and geophysics [ 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 ]. Indeed, fractional derivatives capture memory effects [ 43 ] and hereditary properties, providing a more insightful description of the phenomena [ 31 , 44 , 45 , 46 ].…”

Section: Introductionmentioning

confidence: 99%

Entropy Analysis of Soccer Dynamics

Lopes

Machado

2019

Entropy

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This paper adopts the information and fractional calculus tools for studying the dynamics of a national soccer league. A soccer league season is treated as a complex system (CS) with a state observable at discrete time instants, that is, at the time of rounds. The CS state, consisting of the goals scored by the teams, is processed by means of different tools, namely entropy, mutual information and Jensen–Shannon divergence. The CS behavior is visualized in 3-D maps generated by multidimensional scaling. The points on the maps represent rounds and their relative positioning allows for a direct interpretation of the results.

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“…The tools to analyze complex systems have been successfully adopted in different areas, including economics, life and social sciences [ 15 ], with the objective of finding fundamental principles and universalities that govern the systems’ dynamics [ 16 , 17 ]. Complexity is helpful to quantitatively describe nonlinear systems and to detect changes in their dynamics.…”

Section: Introductionmentioning

confidence: 99%

Complexity Analysis of Escher’s Art

Lopes

Machado

2019

Entropy

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Art is the output of a complex system based on the human spirit and driven by several inputs that embed social, cultural, economic and technological aspects of a given epoch. A solid quantitative analysis of art poses considerable difficulties and reaching assertive conclusions is a formidable challenge. In this paper, we adopt complexity indices, dimensionality-reduction and visualization techniques for studying the evolution of Escher’s art. Grayscale versions of 457 artworks are analyzed by means of complexity indices and represented using the multidimensional scaling technique. The results are correlated with the distinct periods of Escher’s artistic production. The time evolution of the complexity and the emergent patterns demonstrate the effectiveness of the approach for a quantitative characterization of art.

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Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

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Cited by 47 publications

References 48 publications

Fractional Dynamics and Pseudo-Phase Space of Country Economic Processes

Fractional Dynamics and Pseudo-Phase Space of Country Economic Processes

Entropy Analysis of Soccer Dynamics

Complexity Analysis of Escher’s Art

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