Abstract
The human brain constitutes one of the most advanced networks produced by nature, consisting of billions of neurons communicating with each other. However, this communication is not in real-time, with different communication or time-delays occurring between neurons in different brain areas. Here, we investigate the impacts of these delays by modeling large interacting neural circuits as neural-field systems which model the bulk activity of populations of neurons. By using a Master Stability Function analysis combined with numerical simulations, we find that delays (1) may actually stabilize brain dynamics by temporarily preventing the onset to oscillatory and pathologically synchronized dynamics and (2) may enhance or diminish synchronization depending on the underlying eigenvalue spectrum of the connectivity matrix. Real eigenvalues with large magnitudes result in increased synchronizability while complex eigenvalues with large magnitudes and positive real parts yield a decrease in synchronizability in the delay vs. instantaneously coupled case. This result applies to networks with fixed, constant delays, and was robust to networks with heterogeneous delays. In the case of real brain networks, where the eigenvalues are predominantly real, owing to the nearly symmetric nature of these weight matrices, biologically plausible, small delays, are likely to increase synchronization, rather than decreasing it.
Highlights
Biological systems often form intricate and highly interconnected networks
We show how the presence of small time delays in the coupling influences dynamic behavior and synchronization in comparison to the instantaneously coupled networks.We limit our study to delay magnitudes that are biologically relevant; these are small in comparison with other time scales in the model
The preliminary simulations display some link to qualitative behaviors of the instantaneous case but with differences in the behavior of the delayed vs. non-delayed networks for otherwise identical parameter values
Summary
Biological systems often form intricate and highly interconnected networks. Examples include the chemical reaction networks present within a single cell at the small scale (Kitano, 2002), the spread of disease through social networks (Keeling and Eames, 2005) or ecological networks across entire biomes or even the planet itself at the large scale (Montoya et al, 2006). One of the critical defining features in these networks is that communication from putative nodes is seldom instantaneous, and is often plagued by delays. Nowhere is this clearer than in the human brain, an intricate network of neurons limited by the slow propagation speed of action potentials or spikes, which can take up to milliseconds to transmit information across areas (Roxin et al, 2005; Ghosh et al, 2008; Deco et al, 2009). Pathologically strong synchrony exists in neurological disorders such as epilepsy despite the presence of time-delays (Uhlhaas and Singer, 2006). The presence of delays alone can have variable impacts on synchronization with synchronizability determined by (1) the topology of the network, (2) the dynamics of the nodes, and (3) the nature of the delays
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