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Article

Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis

by
Roberto C. Budzinski
*,
Bruno Rafael Reichert Boaretto
,
Thiago L. Prado
and
Sergio Roberto Lopes
Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, PR, Brazil
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(2), 42; https://doi.org/10.3390/mca24020042
Submission received: 18 March 2019 / Revised: 10 April 2019 / Accepted: 17 April 2019 / Published: 20 April 2019
(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)
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Abstract

The study of synchronization in complex networks is useful for understanding a variety of systems, including neural systems. However, the properties of the transition to synchronization are still not well known. In this work, we analyze the details of the transition to synchronization in complex networks composed of bursting oscillators under small-world and scale-free topologies using recurrence quantification analysis, specifically the determinism. We demonstrate the existence of non-stationarity states in the transition region. In the small-world network, the transition region denounces the existence of two-state intermittency.
Keywords: neural network; synchronization; nonlinear dynamics neural network; synchronization; nonlinear dynamics

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MDPI and ACS Style

Budzinski, R.C.; Boaretto, B.R.R.; Prado, T.L.; Lopes, S.R. Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis. Math. Comput. Appl. 2019, 24, 42. https://doi.org/10.3390/mca24020042

AMA Style

Budzinski RC, Boaretto BRR, Prado TL, Lopes SR. Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis. Mathematical and Computational Applications. 2019; 24(2):42. https://doi.org/10.3390/mca24020042

Chicago/Turabian Style

Budzinski, Roberto C., Bruno Rafael Reichert Boaretto, Thiago L. Prado, and Sergio Roberto Lopes. 2019. "Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis" Mathematical and Computational Applications 24, no. 2: 42. https://doi.org/10.3390/mca24020042

APA Style

Budzinski, R. C., Boaretto, B. R. R., Prado, T. L., & Lopes, S. R. (2019). Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis. Mathematical and Computational Applications, 24(2), 42. https://doi.org/10.3390/mca24020042

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