Neuron dynamics variability and anomalous phase synchronization of neural networks

Abstract

Anomalous phase synchronization describes a synchronization phenomenon occurring even for the weakly coupled network and characterized by a non-monotonous dependence of the synchronization strength on the coupling strength. Its existence may support a theoretical framework to some neurological diseases, such as Parkinson’s and some episodes of seizure behavior generated by epilepsy. Despite the success of controlling or suppressing the anomalous phase synchronization in neural networks applying external perturbations or inducing ambient changes, the origin of the anomalous phase synchronization as well as the mechanisms behind the suppression is not completely known. Here, we consider networks composed of N=2000 coupled neurons in a small-world topology for two well known neuron models, namely, the Hodgkin-Huxley-like and the Hindmarsh-Rose models, both displaying the anomalous phase synchronization regime. We show that the anomalous phase synchronization may be related to the individual behavior of the coupled neurons; particularly, we identify a strong correlation between the behavior of the inter-bursting-intervals of the neurons, what we call neuron variability, to the ability of the network to depict anomalous phase synchronization. We corroborate the ideas showing that external perturbations or ambient parameter changes that eliminate anomalous phase synchronization and at the same time promote small changes in the individual dynamics of the neurons, such that an increasing individual variability of neurons implies a decrease of anomalous phase synchronization. Finally, we demonstrate that this effect can be quantified using a well known recurrence quantifier, the “determinism.” Moreover, the results obtained by the determinism are based on only the mean field potential of the network, turning these measures more suitable to be used in experimental situations.

Suppression of Phase Synchronization in Scale-Free Neural Networks Using External Pulsed Current Protocols

“…It was shown that the scale-free network displays a non-monotonic evolution of the phase synchronization as the coupling between neurons increases. A similar scenario has been observed in small-world networks, which is called "anomalous phase synchronization" [30,31,55], since the traditional behavior should monotonically transition to PS [33]. Especially, Parkinson's disease and some episodes of seizure behavior generated by epilepsy may be associated to anomalous synchronization.…”

“…We showed the existence of a threshold, 2000 neurons (40% of the network), which must be disturbed to reach the suppression of anomalous PS in all cases. Such a conclusion implies that the synchronization is related to the individual dynamics of each neuron rather than the network topology [33].…”

“…In this paper, we model a neural network composed of N = 5000 Hodgkin-Huxley-type neurons to study the synchronization phenomena. A similar approach have been used to analyze small-world neural networks [31,33,55]. However, the influence of topology plays an important role in the synchronization characteristics [22,35,38].…”

“…In fact, this kind of behavior has also been observed in non-identical coupled Rösller oscillators [32]. Recently, the mechanism behind the abnormal synchronization in a neural network composed of bursting neurons is explored and the relationship between the individual neuron behavior and the network synchronization helps to understand the phenomenon [33,34]. In [33], it is shown that the occurring of abnormal synchronization is related to the periodic inter-burst interval of the uncoupled neuron.…”

“…Recently, the mechanism behind the abnormal synchronization in a neural network composed of bursting neurons is explored and the relationship between the individual neuron behavior and the network synchronization helps to understand the phenomenon [33,34]. In [33], it is shown that the occurring of abnormal synchronization is related to the periodic inter-burst interval of the uncoupled neuron. Besides that, in [34], it is observed that the abnormal synchronization occurs due to an interplay between the periodic individual behavior and the influence of coupling strength, which is strong enough to induce the network to phase synchronization without destroying the influence of individual periodic behavior.…”