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.
Highlights
Over the past decades, a number of observations of chaos have been reported in the analysis of time series from a variety of neural systems, ranging from the simplest to the more complex[1,2]
The results of Functional Connectivity Dynamics (FCD) analysis show that chaotic nodes can promote what is known as the multi-stable behaviour, where the network dynamically switches between a number of different semi-synchronized, metastable states
We use a model of neural oscillator that can display either chaotic or non-chaotic behaviour depending on the parameters (Figs 1 and 2A, see12)
Summary
A number of observations of chaos have been reported in the analysis of time series from a variety of neural systems, ranging from the simplest to the more complex[1,2]. It is generally accepted that the inherent instability of chaos in nonlinear systems dynamics, facilitates the extraordinary ability of neural systems to respond quickly to changes in their external inputs[3], to make transitions from one pattern of behaviour to another when the environment is altered[4], and to create a rich variety of patterns endowing neuronal circuits with remarkable computational capabilities[5]. The first type of chaotic dynamics in neural systems is typically accompanied by microscopic chaotic dynamics at the level of individual oscillators The presence of this chaos has been observed in networks of Hindmarsh-Rose neurons[8] and biophysical conductance-based neurons[9,10,11,12]. Taking advantage of the mapping of chaotic regions that we previously performed, we simulated small-world[31] neural networks consisting on a heterogeneous population of HB + Ih neurons, connected by electrical synapses, and sampled their parameters from either chaotic or non-chaotic regions of the parameter space
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