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Nonstationary transition to phase synchronization of neural networks induced by the coupling architecture

Author

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  • Budzinski, R.C.
  • Boaretto, B.R.R.
  • Rossi, K.L.
  • Prado, T.L.
  • Kurths, J.
  • Lopes, S.R.

Abstract

The transition to phase synchronized states of neural networks with bursting dynamics may have nonstationary characteristics, as well as sensitivity to initial conditions. Here, we analyze the paradigmatic network composed of neurons of Rulkov to investigate dynamic properties of the transitions to phase synchronization displayed by networks under two different topologies of the connection matrices, namely, small-world and random ones. Our analyses of both connection architectures reveal that neural networks under small-world topology display higher sensibility to initial conditions, and contrarily to the random connection case, depict a nonstationary transition to phase synchronization through the presence of a two-state on–off intermittency. The analyses are based on the recurrence quantifier determinism calculated by using only the local (mean) field potential (LFP) of the network, an experimentally easy accessible data. The use of LFP data offers advantages in the quantification of the nonstationary dynamics at the transition to phase synchronized states, since the more traditional Kuramoto order parameter must be computed over the individual signals of the neurons.

Suggested Citation

  • Budzinski, R.C. & Boaretto, B.R.R. & Rossi, K.L. & Prado, T.L. & Kurths, J. & Lopes, S.R., 2018. "Nonstationary transition to phase synchronization of neural networks induced by the coupling architecture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 321-334.
  • Handle: RePEc:eee:phsmap:v:507:y:2018:i:c:p:321-334
    DOI: 10.1016/j.physa.2018.05.076
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    References listed on IDEAS

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    1. M. E. J. Newman & D. J. Watts, 1999. "Scaling and Percolation in the Small-World Network Model," Working Papers 99-05-034, Santa Fe Institute.
    2. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
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    1. Budzinski, R.C. & Boaretto, B.R.R. & Prado, T.L. & Lopes, S.R., 2019. "Temperature dependence of phase and spike synchronization of neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 35-42.

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