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Mathematical and computational modeling of political systems

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Abstract

This paper proposes a new modeling approach for describing the dynamics of political systems. For that purpose, real-world data series from several countries is considered. More specifically, democratic systems of six European countries involving elections that produce a parliament supporting the government are analyzed. First, the information is processed by means of multidimensional scaling and computational visualization techniques. Second, an analogy toward multi-particle systems is formulated, leading to an interpretation close to those adopted in physics.

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Acknowledgements

The author thanks the help of the following colleagues in collecting and understanding the raw data from their countries: Robin De Keyser, Anastasios Lazopoulos, Dariusz Brzeziński, Juan Luis Garcia Girao, António Vega, and Mohamed Torbati.

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Authors and Affiliations

  1. Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015, Porto, Portugal

    J. Tenreiro Machado

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  1. J. Tenreiro Machado
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Correspondence to J. Tenreiro Machado.

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Appendix

Appendix

See Tables 2, 3, 4, 5, 6 and 7.

Table 2 Number of seats \(n_i(t_k)\), \(i=1,\ldots ,7\), \(k=1,\ldots ,12\), of the parties versus election time (in years) for Belgium during period 1977–2014
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Table 3 Number of seats \(n_i(t_k)\), \(i=1,\ldots ,5\), \(k=1,\ldots ,17\), of the parties versus election time (in years) for Greece during period 1974–2015
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Table 4 Number of seats \(n_i(t_k)\), \(i=1,\ldots ,7\), \(k=1,\ldots ,8\), of the parties versus election time (in years) for Poland during period 1991–2015
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Table 5 Number of seats \(n_i(t_k)\), \(i=1,\ldots ,6\), \(k=1,\ldots ,11\), of the parties versus election time (in years) for Portugal during period 1983–2015
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Table 6 Number of seats \(n_i(t_k)\), \(i=1,\ldots ,9\), \(k=1,\ldots ,13\), of the parties versus election time (in years) for Spain during period 1977–2016
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Table 7 Number of seats \(n_i(t_k)\), \(i=1,\ldots ,4\), \(k=1,\ldots ,27\), of the parties versus election time (in years) for the UK during period 1918–2017
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Machado, J.T. Mathematical and computational modeling of political systems. Nonlinear Dyn 96, 1471–1490 (2019). https://doi.org/10.1007/s11071-019-04865-2

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