Modular Neuronal Network Research Articles

Diversity and time delays induce resonance in a modular neuronal network.

This paper focuses on the resonance dynamics of a modular neuronal network consisting of several small-world subnetworks. The considered network is composed of delay-coupled FitzHugh-Nagumo (FHN) neurons, whose characteristic parameters present diversity in the form of quenched noise. Our numerical results indicate that when such a network is subjected to an external subthreshold periodic signal, its collective response is optimized for an intermediate level of diversity, namely, a resonant behavior can be induced by an appropriate level of diversity. How the probabilities of intramodule and intermodule connections, as well as the number of subnetworks influence the diversity-induced resonance are also discussed. Further, conclusive evidences demonstrate the nontrivial role of time-delayed coupling on the diversity-induced resonance properties. Especially, multiple resonance is obviously detected when time delays are located at integer multiples of the oscillation period of the signal. Moreover, the phenomenon of fine-tuned delays in inducing multiple resonance remains when diversity is within an intermediate range. Our findings have implications that neural systems may profit from their generic diversity and delayed coupling to optimize the response to external stimulus.

Delay-induced synchronization transitions in modular scale-free neuronal networks with hybrid electrical and chemical synapses

We study the dependence of synchronization transitions in modular networks of bursting neurons with hybrid electrical–chemical synapses on the information transmission delay and the probability of electrical synapses. The modular network is composed of subnetworks (clusters); each of them presents the scale-free property. It is shown that, irrespective of the probability of electrical synapses, the time delay can always induce synchronization transitions in modular neuronal networks. Regions of synchronization and non-synchronization appear intermittently as the delay increases. In particular, all these transitions to burst synchronization occur approximately at integer multiples of oscillatory period of individual neurons. In addition, for larger probability of electrical synapses, the intermittent synchronization transition is more profound, due to the stronger synchronization capability of electrical synapses compared with chemical ones. Furthermore, the transition to synchronous bursting can also be induced by the variation of modular network parameters, that is, the coupling strength between neurons, the interconnection probability between different subnetworks, as well as the number of subnetworks. Particularly, we find that a modular neuronal network is harder to get global synchronization when constituting neurons are dispersed over more clusters. On the other hand, chemical and electrical synapses can perform complementary roles in the synchronization of hybrid modular neuronal networks: the larger the electrical synapse strength is the smaller the chemical synapse strength needed to achieve burst synchronization.

Impact of delays on the synchronization transitions of modular neuronal networks with hybrid synapses

The combined effects of the information transmission delay and the ratio of the electrical and chemical synapses on the synchronization transitions in the hybrid modular neuronal network are investigated in this paper. Numerical results show that the synchronization of neuron activities can be either promoted or destroyed as the information transmission delay increases, irrespective of the probability of electrical synapses in the hybrid-synaptic network. Interestingly, when the number of the electrical synapses exceeds a certain level, further increasing its proportion can obviously enhance the spatiotemporal synchronization transitions. Moreover, the coupling strength has a significant effect on the synchronization transition. The dominated type of the synapse always has a more profound effect on the emergency of the synchronous behaviors. Furthermore, the results of the modular neuronal network structures demonstrate that excessive partitioning of the modular network may result in the dramatic detriment of neuronal synchronization. Considering that information transmission delays are inevitable in intra- and inter-neuronal networks communication, the obtained results may have important implications for the exploration of the synchronization mechanism underlying several neural system diseases such as Parkinson's Disease.

The effects of time delay on the synchronization transitions in a modular neuronal network with hybrid synapses

Delay-induced synchronization transitions are studied in a modular neuronal network of small-world subnetworks with hybrid synapses in this paper. Numerical results show that the spatiotemporal synchronization transitions in a modular neuronal network not only depend on the information transmission delay, but also can be induced by the variations of the probability of inhibitory synapses and the number of subnetworks in the modular networks. In the hybrid modular network, the information transmission delay is shown to be significant, which can either promote or destroy synchronization of neuronal activity. In particular, the increasing delays can induce the intermittent appearance of regions of synchronization and non-synchronization. Interestingly, it is found that intermittent synchronization transition is relatively profound for smaller and larger probability of inhibitory synapses, while synchronization transition seems less profound for the moderate probability of inhibitory synapses. In addition, if only the delay is appropriate, there exists a suitable modular network topology structure enhancing the synchronized neuronal activity.

Stochastic resonance on a modular neuronal network of small-world subnetworks with a subthreshold pacemaker

We study the phenomenon of stochastic resonance on a modular neuronal network consisting of several small-world subnetworks with a subthreshold periodic pacemaker. Numerical results show that the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the intensity of additive spatiotemporal noise. This effect of pacemaker-driven stochastic resonance of the system depends extensively on the local and the global network structure, such as the intra- and inter-coupling strengths, rewiring probability of individual small-world subnetwork, the number of links between different subnetworks, and the number of subnetworks. All these parameters play a key role in determining the ability of the network to enhance the noise-induced outreach of the localized subthreshold pacemaker, and only they bounded to a rather sharp interval of values warrant the emergence of the pronounced stochastic resonance phenomenon. Considering the rather important role of pacemakers in real-life, the presented results could have important implications for many biological processes that rely on an effective pacemaker for their proper functioning.

Chaotic phase synchronization in a modular neuronal network of small-world subnetworks

We investigate the onset of chaotic phase synchronization of bursting oscillators in a modular neuronal network of small-world subnetworks. A transition to mutual phase synchronization takes place on the bursting time scale of coupled oscillators, while on the spiking time scale, they behave asynchronously. It is shown that this bursting synchronization transition can be induced not only by the variations of inter- and intra-coupling strengths but also by changing the probability of random links between different subnetworks. We also analyze the effect of external chaotic phase synchronization of bursting behavior in this clustered network by an external time-periodic signal applied to a single neuron. Simulation results demonstrate a frequency locking tongue in the driving parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this synchronization region increases with the signal amplitude and the number of driven neurons but decreases rapidly with the network size. Considering that the synchronization of bursting neurons is thought to play a key role in some pathological conditions, the presented results could have important implications for the role of externally applied driving signal in controlling bursting activity in neuronal ensembles.