Is chaos making a difference? Synchronization transitions in chaotic and non-chaotic neuronal networks

Chaotic dynamics of neural oscillations has been shown at the single neuron and network levels, both in experimental data and numerical simulations. Theoretical studies over the last twenty years have demonstrated an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to relevant network behavior and whether the dynamical richness of neural networks are sensitive to the dynamics of isolated neurons, still remain open questions. We investigated transition dynamics of a medium-sized heterogeneous neural network of neurons connected by electrical coupling in a small world topology. We make use of an oscillatory neuron model (HB+Ih) that exhibits either chaotic or non-chaotic behavior at different combinations of conductance parameters. Measuring order parameter as a measure of synchrony, we find that the heterogeneity of firing rate and types of firing patterns make a greater contribution than chaos to the steepness of synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in process of network synchronization transitions. Moreover, the 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 the multi-stable behavior, where the network dynamically switches between a number of different semi-synchronized, metastable states.