Recurrence quantification analysis for the identification of burst phase synchronisation

Author(s):Show less -

Lameu, E. L. ^{[1, 2]} ; Yanchuk, S. ^[3] ; Macau, E. E. N. ^{[2, 4]} ; Borges, F. S. ^[5] ; Iarosz, K. C. ^{[1, 6, 7, 8]} ; Caldas, I. L. ^[8] ; Protachevicz, P. R. ^[9] ; Borges, R. R. ^[10] ; Viana, R. L. ^[11] ; Szezech, Jr., J. D. ^{[9, 12]} ; Batista, A. M. ^{[6, 7, 8, 9, 12]} ; Kurths, J. ^{[1, 6]}

Affiliation:Show less -

^[1] Humboldt Univ, Dept Phys, D-12489 Berlin - Germany

^[2] Natl Inst Space Res, BR-12227010 Sao Jose Dos Campos, SP - Brazil

^[3] Tech Univ Berlin, Inst Math, D-10623 Berlin - Germany

^[4] Univ Fed Sao Paulo, ICT Inst Sci & Technol, BR-12231280 Sao Jose Dos Campos, SP - Brazil

^[5] Fed Univ ABC, Ctr Math Computat & Cognit, BR-09606045 Sao Bernardo Do Campo, SP - Brazil

^[6] Potsdam Inst Climate Impact Res, D-14473 Potsdam - Germany

^[7] Univ Aberdeen, SUPA, Inst Complex Syst & Math Biol, Aberdeen AB24 3UE - Scotland

^[8] Univ Sao Paulo, Inst Phys, BR-05508900 Sao Paulo - Brazil

^[9] Univ Estadual Ponta Grossa, Program Postgraduat Sci, BR-84030900 Ponta Grossa, Parana - Brazil

^[10] Univ Tecnol Fed Parana, Dept Math, BR-84016210 Ponta Grossa, Parana - Brazil

^[11] Univ Fed Parana, Dept Phys, BR-80060000 Curitiba, Parana - Brazil

^[12] Univ Estadual Ponta Grossa, Dept Math & Stat, BR-84030900 Ponta Grossa, Parana - Brazil

• Document type: Journal article
• Source: Chaos; v. 28, n. 8 AUG 2018.
• Web of Science Citations: 3

Abstract

In this work, we apply the spatial recurrence quantification analysis (RQA) to identify chaotic burst phase synchronisation in networks. We consider one neural network with small-world topology and another one composed of small-world subnetworks. The neuron dynamics is described by the Rulkov map, which is a two-dimensional map that has been used to model chaotic bursting neurons. We show that with the use of spatial RQA, it is possible to identify groups of synchronised neurons and determine their size. For the single network, we obtain an analytical expression for the spatial recurrence rate using a Gaussian approximation. In clustered networks, the spatial RQA allows the identification of phase synchronisation among neurons within and between the subnetworks. Our results imply that RQA can serve as a useful tool for studying phase synchronisation even in networks of networks. Published by AIP Publishing. (AU)

• FAPESP's process: 17/18977-1 - Analysis of Electrical Synapses Contribution in Neuronal Synchronization
• Grantee: Fernando da Silva Borges
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 17/20920-8 - Plasticity in neuronal networks
• Grantee: Kelly Cristiane Iarosz
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 16/23398-8 - Synaptic plasticity in neuronal networks with time delay
• Grantee: Ewandson Luiz Lameu
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 15/07311-7 - Dynamic behaviour of neural networks
• Grantee: Kelly Cristiane Iarosz
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 17/13502-5 - Synchronisation in time-delayed networks with synaptic plasticity
• Grantee: Ewandson Luiz Lameu
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 15/50122-0 - Dynamic phenomena in complex networks: basics and applications
• Grantee: Elbert Einstein Nehrer Macau
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 11/19296-1 - Nonlinear dynamics
• Grantee: Iberê Luiz Caldas
• Support Opportunities: Research Projects - Thematic Grants