Phase synchronization in a sparse network of randomly connected neurons under the effect of Poissonian spike inputs

Bruno R R Boaretto; Paulo R Protachevicz; Matheus Hansen; Jonas Oliveira; Alexandre C Andreani; Elbert E N Macau

doi:10.1063/5.0179912

Phase synchronization in a sparse network of randomly connected neurons under the effect of Poissonian spike inputs

Chaos. 2023 Dec 1;33(12):123115. doi: 10.1063/5.0179912.

Authors

Bruno R R Boaretto¹, Paulo R Protachevicz^{2

3}, Matheus Hansen⁴, Jonas Oliveira⁵, Alexandre C Andreani^{1

6}, Elbert E N Macau¹

Affiliations

¹ Institute of Science and Technology, Universidade Federal de São Paulo, 12247-014 São José dos Campos, São Paulo, Brazil.
² Physics Institute, University of São Paulo, 05508-090 São Paulo, São Paulo, Brazil.
³ Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, AB24 3UE Aberdeen, United Kingdom.
⁴ Center for Mathematics and Applications (NOVA Math), NOVA School of Science and Technology, Universidade NOVA de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal.
⁵ National Institute for Space Research, 12227-010 São José dos Campos, São Paulo, Brazil.
⁶ Federal Institute of São Paulo, 12322-030 Jacareí, São Paulo, Brazil.

PMID: 38079646
DOI: 10.1063/5.0179912

Abstract

This article investigates the emergence of phase synchronization in a network of randomly connected neurons by chemical synapses. The study uses the classic Hodgkin-Huxley model to simulate the neuronal dynamics under the action of a train of Poissonian spikes. In such a scenario, we observed the emergence of irregular spikes for a specific range of conductances and also that the phase synchronization of the neurons is reached when the external current is strong enough to induce spiking activity but without overcoming the coupling current. Conversely, if the external current assumes very high values, then an opposite effect is observed, i.e., the prevention of the network synchronization. We explain such behaviors considering different mechanisms involved in the system, such as incoherence, minimization of currents, and stochastic effects from the Poissonian spikes. Furthermore, we present some numerical simulations where the stimulation of only a fraction of neurons, for instance, can induce phase synchronization in the non-stimulated fraction of the network, besides cases in which for larger coupling values, it is possible to propagate the spiking activity in the network when considering stimulation over only one neuron.