Synchronization transitions on scale-free neuronal networks due to finite information transmission delays

Abstract

We investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale-free neuronal networks with different average degrees and scaling exponents. As the underlying model of neuronal dynamics, we use the efficient Rulkov map with additive noise. We show that increasing the coupling strength enhances synchronization monotonously, whereas delay plays a more subtle role. In particular, we found that depending on the inherent oscillation frequency of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions manifest as well-expressed minima in the measure for spatial synchrony, appearing at every multiple of the oscillation frequency. Larger coupling strengths or average degrees can broaden the region of regular propagating fronts by a given information transmission delay and further improve synchronization. These results are robust against variations in system size, intensity of additive noise, and the scaling exponent of the underlying scale-free topology. We argue that fine-tuned information transmission delays are vital for assuring optimally synchronized excitatory fronts on complex neuronal networks and, indeed, they should be seen as important as the coupling strength or the overall density of interneuronal connections. We finally discuss some biological implications of the presented results.

Spatiotemporal dynamics on small-world neuronal networks: The roles of two types of time-delayed coupling

“…People have found that time delay through electric synapse can facilitate and enhance neuronal synchronization [36][37][38], induce various spatiotemporal patterns [39], enhance spatiotemporal order in coupled noisy small-world neuronal networks [40]. In addition, Perc and his cooperators have contributed some remarkable findings in this field, they found that information transmission delay can induce transition from zigzag fronts to clustering anti-phase synchronization [41] and further to regular in-phase synchronization on small-world neuronal networks [42], intermittently induce synchronization transitions on scale-free neuronal networks [44,46]. Furthermore, they also showed that delay can enhance coherence of spatial dynamics in small-world networks of HH neurons [49,50] and induce multiple stochastic resonances on scale-free neuronal networks [51,52], they proved that delay-induced multiple stochastic resonances are robust to the changing of the scale-free networks, even when the nodes of the network are more than 10000.…”

“…A number of interesting effects of time-delayed coupling on the qualitative and quantitative properties of neuronal dynamics have been reported in literature, including both chemical synapse coupling [29][30][31][32][33][34][35] and electric synapse coupling [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52].…”

Spatial evolution of Hindmarsh–Rose neural network with time delays

“…The concept of small-world networks by Watts and Strogatz was also included [1,6]. The recent innovation is the introduction of time delays to network models [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] which allows to study the influence of the limited speed of information processing on the network dynamics. This speed limitation is indeed present in neuronal communication as the action potential propagates with the speed of tens of meters per second which is a significant aspect if the physical size of nerve tissue taken into consideration.…”

Effect of network architecture on burst and spike synchronization in a scale-free network of bursting neurons

“…This kind of SFNs are inhomogeneous ones with a few "hubs" (superconnected nodes), in contrast to statistically homogeneous networks such as random graphs and small-world networks [56,57]. Many recent works on various subjects of neurodynamics (e.g., coupling-induced burst synchronization, delay-induced burst synchronization, and suppression of burst synchronization) have been done in SFNs with a few percent of hub neurons with an exceptionally large number of connections [58][59][60][61][62][63].…”