Detection of nonstationary transition to synchronized states of a neural network using recurrence analyses

R. C. Budzinski, B. R. R. Boaretto, T. L. Prado, and S. R. Lopes
Phys. Rev. E 96, 012320 – Published 25 July 2017
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Abstract

We study the stability of asymptotic states displayed by a complex neural network. We focus on the loss of stability of a stationary state of networks using recurrence quantifiers as tools to diagnose local and global stabilities as well as the multistability of a coupled neural network. Numerical simulations of a neural network composed of 1024 neurons in a small-world connection scheme are performed using the model of Braun et al. [Int. J. Bifurcation Chaos 08, 881 (1998)], which is a modified model from the Hodgkin-Huxley model [J. Phys. 117, 500 (1952)]. To validate the analyses, the results are compared with those produced by Kuramoto's order parameter [Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin Heidelberg, 1984)]. We show that recurrence tools making use of just integrated signals provided by the networks, such as local field potential (LFP) (LFP signals) or mean field values bring new results on the understanding of neural behavior occurring before the synchronization states. In particular we show the occurrence of different stationary and nonstationarity asymptotic states.

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  • Received 26 April 2017

DOI:https://doi.org/10.1103/PhysRevE.96.012320

©2017 American Physical Society

Physics Subject Headings (PhySH)

Interdisciplinary PhysicsNonlinear DynamicsGeneral PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

R. C. Budzinski1, B. R. R. Boaretto1, T. L. Prado2, and S. R. Lopes1,*

  • 1Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, Paraná, Brazil
  • 2Instituto de Engenharia, Ciência e Tecnologia, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 39100-000 Janaúba, Minas Gerais, Brazil

  • *lopes@fisica.ufpr.br

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Issue

Vol. 96, Iss. 1 — July 2017

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