Synchronization transition in neuronal networks composed of chaotic or non-chaotic oscillators

Abstract

Chaotic dynamics has been shown in the dynamics of neurons and neural networks, in experimental data and numerical simulations. Theoretical studies have proposed an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to network behaviour and whether the dynamical richness of neural networks is sensitive to the dynamics of isolated neurons, still remain open questions. We investigated synchronization transitions in heterogeneous neural networks of neurons connected by electrical coupling in a small world topology. The nodes in our model are oscillatory neurons that – when isolated – can exhibit either chaotic or non-chaotic behaviour, depending on conductance parameters. We found that the heterogeneity of firing rates and firing patterns make a greater contribution than chaos to the steepness of the synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in the transition to full synchrony. Moreover, macroscopic chaos is observed regardless of the dynamics nature of the neurons. However, performing a Functional Connectivity Dynamics analysis, we show that chaotic nodes can promote what is known as multi-stable behaviour, where the network dynamically switches between a number of different semi-synchronized, metastable states.

Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis

“…We noted a clear transition from unsynchronized to phase synchronized states where non-stationary behavior was observed in both cases. A similar scenario has been observed in [9,11,26,27,69]. Despite the higher number of connections in the small-world case, the transition region and the phase synchronized states were observed for smaller values of coupling strength in the scale-free case.…”

“…Regarding complex networks, it is known that this kind of system can show emergent behavior, where the global behavior observed is richer than the sum of the individual element behaviors. In this way, the existence of non-monotonic transitions to synchronization as a function of coupling strength in neural networks [26][27][28][29][30], where non-stationary states can be noticed, has been reported in the literature. In some cases, in the transition region, on-off intermittency in the two states has been observed, where the network displays the existence of two locally stable states but globally unstable ones [18,26], as defined in [31].…”

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

“…It is observed in the literature that a neural network under a small-world topology can display abnormal phase synchronization for weak coupling regime since the phase synchronization regime in this region is characterized by a non-monotonic evolution of synchronization levels as a function of the coupling between neurons [29][30][31]. In fact, this kind of behavior has also been observed in non-identical coupled Rösller oscillators [32].…”

Noise-driven multistability vs deterministic chaos in phenomenological semi-empirical models of whole-brain activity

“…In particular, a Maximal Lyapunov exponent (MLE) greater than zero is widely used as an indicator of chaos 71 . To assess the chaotic behavior of the network of coupled Rossler oscillators we calculated the MLE from trajectories in the full variable space, following a standard numerical method published by Sprott 72,73 .…”