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Dependence on the local dynamics of a network phase synchronization process

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  • Cambraia, E.B.S.A.
  • Flauzino, J.V.V.
  • Prado, T.L.
  • Lopes, S.R.

Abstract

Partial phase synchronization, also reported as neuron cooperation, is a pivotal behavior of the brain and related to its main features, such as memory. The excess or even the lack of phase synchronization are associated with brain disorders like epilepsy and Parkinson’s disease. These diseases may be related to malfunctioning of the synchronization process of the neurons, triggered by changes of the local dynamics of the neurons influenced by parameters such as the ion-channel conductance. In fact, it is common to change the local neuron dynamics, using drugs to block or activate specific channels, changing the conductance and bringing the synchronization process to some desired behavior. Here we show that there are two distinct mechanisms leading to network phase synchronized states. The first one is strongly affected by the individual neuron dynamics. In this case, the synchronous state of the network may occur for low values of the coupling, regardless of the network topology. The second synchronized state is induced by the network coupling, in this case the network coupling strength promotes synchronized global states, we say it is a network driver synchronization. We report here how individual characteristics of the local dynamics of the neurons, such as their linear stability, when coupled in a network may be a fundamental player in the phase synchronization process as a function of the coupling strength. Global and small-world topologies are considered for a Hindmarsh–Rose-neuron network. For both coupling schemes, the effects of the local dynamics are clear, inducing early or retarding the occurrence of partial phase synchronization of the network when the coupling strength is varied. In this scenario, we discuss the effect of the local dynamics of the neuron, showing it may be of fundamental importance to understand and control the process of the network phase synchronization. The study also brings useful information to the general understanding of network-phase-synchronization processes.

Suggested Citation

  • Cambraia, E.B.S.A. & Flauzino, J.V.V. & Prado, T.L. & Lopes, S.R., 2023. "Dependence on the local dynamics of a network phase synchronization process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    • Handle: RePEc:eee:phsmap:v:619:y:2023:i:c:s0378437123003059
    DOI: 10.1016/j.physa.2023.128750
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    References listed on IDEAS

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    1. Boaretto, B.R.R. & Budzinski, R.C. & Prado, T.L. & Kurths, J. & Lopes, S.R., 2018. "Suppression of anomalous synchronization and nonstationary behavior of neural network under small-world topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 126-138.
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    5. Xiaoge Bao & Qitong Hu & Peng Ji & Wei Lin & Jürgen Kurths & Jan Nagler, 2022. "Impact of basic network motifs on the collective response to perturbations," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
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