Information Transmission Delay Research Articles

The consensus problem in networks with transmission delays

We study discrete- and continuous-time consensus problems on networks in the presence of distributed time delays. We focus on information transmission delays, as opposed to information processing delays, so that each node of the network compares its current state with the past states of its neighbours. We consider directed and weighted networks where the connection structure is described by a normalized Laplacian matrix and show that consensus is achieved if and only if the underlying graph contains a directed spanning tree. This statement holds independently of the transmission delays, which is in contrast to the case of processing delays. Furthermore, we calculate the consensus value explicitly, and show that it is determined by the history of the system over an interval of time, unlike the case of processing delays where the consensus value depends only on the initial state of the system at time zero. This provides the consensus algorithm with improved robustness against noise.

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.

Delay-induced synchronization transitions in small-world neuronal networks with hybrid electrical and chemical synapses

We study the dependence of synchronization transitions in small-world networks of bursting neurons with hybrid electrical–chemical synapses on the information transmission delay, the probability of electrical synapses, and the rewiring probability. It is shown that, irrespective of the probability of electrical synapses, the information transmission delay can always induce synchronization transitions in small-world neuronal networks, i.e., regions of synchronization and nonsynchronization appear intermittently as the delay increases. In particular, all these transitions to burst synchronization occur approximately at integer multiples of the bursting period of individual neurons. In addition, for larger probability of electrical synapses, the intermittent synchronization transition is more profound, due to the stronger synchronization ability of electrical synapses compared with chemical ones. More importantly, chemical and electrical synapses can perform complementary roles in the synchronization of hybrid small-world neuronal networks: the larger the electrical synapse strength is, the smaller the chemical synapse strength needed to achieve burst synchronization. Furthermore, the small-world topology has a significant effect on the synchronization transition in hybrid neuronal networks. It is found that increasing the rewiring probability can always enhance the synchronization of neuronal activity. The results obtained are instructive for understanding the synchronous behavior of neural systems.

Stimulus-induced transition of clustering firings in neuronal networks with information transmission delay

We study the evolution of spatiotemporal dynamics and transition of clustering firing synchronization on spiking Hodgkin-Huxley neuronal networks as information transmission delay and the periodic stimulus are varied. In particular, it is shown that the tuned information transmission delay can induce a clustering anti-phase synchronization transition with the pacemaker, where two equal clusters can alternatively synchronize in anti-phase firing. More interestingly, we show that the periodic stimulus can drive the delay-induced clustering anti-phase firing synchronization bifurcate to the collective perfect synchronization, which is routed by the complex process including collective chaotic firings and clustering out-of-phase synchronization of the neuronal networks. In addition, the periodic stimulus induced clustering firings of the spiking neuronal networks are robust to the connectivity probability of small world networks. Furthermore, the different stimulus frequency induced complexity is also investigated. We hope that the results of this paper can provide insights that could facilitate the understanding of the joint impact of information transmission delays and periodic stimulus on controlling dynamical behaviors of realistic neuronal networks.

Effects of time delay on the stochastic resonance in small-world neuronal networks

The effects of time delay on stochastic resonance in small-world neuronal networks are investigated. Without delay, an intermediate intensity of additive noise is able to optimize the temporal response of the neural system to the subthreshold periodic signal imposed on all neurons constituting the network. The time delay in the coupling process can either enhance or destroy stochastic resonance of neuronal activity in the small-world network. In particular, appropriately tuned delays can induce multiple stochastic resonances, which appear intermittently at integer multiples of the oscillation period of weak external forcing. It is found that the delay-induced multiple stochastic resonances are most efficient when the forcing frequency is close to the global-resonance frequency of each individual neuron. Furthermore, the impact of time delay on stochastic resonance is largely independent of the small-world topology, except for resonance peaks. Considering that information transmission delays are inevitable in intra- and inter-neuronal communication, the presented results could have important implications for the weak signal detection and information propagation in neural systems.

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.

Effect of the heterogeneous neuron and information transmission delay on stochastic resonance of neuronal networks

We study the effect of heterogeneous neuron and information transmission delay on stochastic resonance of scale-free neuronal networks. For this purpose, we introduce the heterogeneity to the specified neuron with the highest degree. It is shown that in the absence of delay, an intermediate noise level can optimally assist spike firings of collective neurons so as to achieve stochastic resonance on scale-free neuronal networks for small and intermediate α(h), which plays a heterogeneous role. Maxima of stochastic resonance measure are enhanced as α(h) increases, which implies that the heterogeneity can improve stochastic resonance. However, as α(h) is beyond a certain large value, no obvious stochastic resonance can be observed. If the information transmission delay is introduced to neuronal networks, stochastic resonance is dramatically affected. In particular, the tuned information transmission delay can induce multiple stochastic resonance, which can be manifested as well-expressed maximum in the measure for stochastic resonance, appearing every multiple of one half of the subthreshold stimulus period. Furthermore, we can observe that stochastic resonance at odd multiple of one half of the subthreshold stimulus period is subharmonic, as opposed to the case of even multiple of one half of the subthreshold stimulus period. More interestingly, multiple stochastic resonance can also be improved by the suitable heterogeneous neuron. Presented results can provide good insights into the understanding of the heterogeneous neuron and information transmission delay on realistic neuronal networks.

Delay-induced synchronization transitions in small-world neuronal networks with hybrid synapses

We study delay-induced synchronization transitions in small-world networks of bursting neurons with hybrid excitatory-inhibitory synapses. Numerical results show that transitions of the spatiotemporal synchrony of neurons can be induced not only by the variations of the information transmission delay but also by changing the probability of inhibitory synapses and the rewiring probability. The delay can either promote or destroy synchronization of neuronal activity in the hybrid small-world neuronal network. In particular, regions of synchronization and nonsynchronization appear intermittently as the delay increases. In addition, for smaller and higher probability of inhibitory synapses, the intermittent synchronization transition is relative profound, while for the moderate probability of inhibitory synapses, synchronization transition seems less profound. More importantly, it is found that a suitable rewired network topology can always enhance the synchronized neuronal activity if only the delay is appropriate.

Impairments of Social Motor Coordination in Schizophrenia

It has been demonstrated that motor coordination of interacting people plays a crucial role in the success of social exchanges. Abnormal movements have been reported during interpersonal interactions of patients suffering from schizophrenia and a motor coordination breakdown could explain this social interaction deficit, which is one of the main and earliest features of the illness. Using the dynamical systems framework, the goal of the current study was (i) to investigate whether social motor coordination is impaired in schizophrenia and (ii) to determine the underlying perceptual or cognitive processes that may be affected. We examined intentional and unintentional social motor coordination in participants oscillating hand-held pendulums from the wrist. The control group consisted of twenty healthy participant pairs while the experimental group consisted of twenty participant pairs that included one participant suffering from schizophrenia. The results showed that unintentional social motor coordination was preserved while intentional social motor coordination was impaired. In intentional coordination, the schizophrenia group displayed coordination patterns that had lower stability and in which the patient never led the coordination. A coupled oscillator model suggests that the schizophrenia group coordination pattern was due to a decrease in the amount of available information together with a delay in information transmission. Our study thus identified relational motor signatures of schizophrenia and opens new perspectives for detecting the illness and improving social interactions of patients.

Effects of information transmission delay and channel blocking on synchronization in scale-free Hodgkin-Huxley neuronal networks

In this paper, we investigate the evolution of spatiotemporal patterns and synchronization transitions in dependence on the information transmission delay and ion channel blocking in scale-free neuronal networks. As the underlying model of neuronal dynamics, we use the Hodgkin-Huxley equations incorporating channel blocking and intrinsic noise. It is shown that delays play a significant yet subtle role in shaping the dynamics of neuronal networks. In particular, regions of irregular and regular propagating excitatory fronts related to the synchronization transitions appear intermittently as the delay increases. Moreover, the fraction of working sodium and potassium ion channels can also have a significant impact on the spatiotemporal dynamics of neuronal networks. As the fraction of blocked sodium channels increases, the frequency of excitatory events decreases, which in turn manifests as an increase in the neuronal synchrony that, however, is dysfunctional due to the virtual absence of large-amplitude excitations. Expectedly, we also show that larger coupling strengths improve synchronization irrespective of the information transmission delay and channel blocking. The presented results are also robust against the variation of the network size, thus providing insights that could facilitate understanding of the joint impact of ion channel blocking and information transmission delay on the spatiotemporal dynamics of neuronal networks.

Stability-Capacity-Adaptive Routing for High-Mobility Multihop Cognitive Radio Networks

In high-mobility cognitive radio networks (CRNs), the fast topology changes increase the complexity of the routing scheme. In this paper, we propose a novel CRN routing scheme that considers the path stability and node capacity. First, a realistic mobility model is proposed to describe the movement of highly mobile airborne nodes [e.g., unmanned aerial vehicles (UAVs)] and estimate the link stability performance based on node movement patterns. Second, we propose a CRN topology management scheme based on a clustering model that considers radio link availability, and the cluster heads (CHs) are selected based on the node degree level, the average number of hops, and channel switching from member nodes to the CH. Third, we propose two new common control channel (CCC) selection schemes based on the node contraction concept and the discrete particle swarm optimization algorithm. The intercluster control channels and gateways are selected from the CHs, considering the average delay of control information transmission between two CHs, as well as the total throughput of control channels. Finally, a novel routing scheme is proposed that tightly integrates with the channel assignment scheme based on the node capacity. Our simulation results show that our proposed CCC selection scheme has high throughput and small transmission time. Compared with other popular CRN routing approaches, our proposed routing scheme achieves lower average end-to-end delay and higher packet delivery ratio for high-mobility CRN applications (such as airborne surveillance).

Taming desynchronized bursting with delays in the Macaque cortical network

Inhibitory coupled bursting Hindmarsh—Rose neurons are considered as constitutive units of the Macaque cortical network. In the absence of information transmission delay the bursting activity is desynchronized, giving rise to spatiotemporally disordered dynamics. This paper shows that the introduction of finite delays can lead to the synchronization of bursting and thus to the emergence of coherent propagating fronts of excitation in the space-time domain. Moreover, it shows that the type of synchronous bursting is uniquely determined by the delay length, with the transitions from one type to the other occurring in a step-like manner depending on the delay. Interestingly, as the delay is tuned close to the transition points, the synchronization deteriorates, which implies the coexistence of different bursting attractors. These phenomena can be observed by different but fixed coupling strengths, thus indicating a new role for information transmission delays in realistic neuronal networks.

Delay-induced intermittent transition of synchronization in neuronal networks with hybrid synapses

We study the dependence of synchronization transitions in scale-free networks of bursting neurons with hybrid synapses on the information transmission delay and the probability of inhibitory synapses. It is shown that, irrespective of the probability of inhibitory synapses, the delay always plays a subtle role during synchronization transition of the scale-free neuronal networks. In particular, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. In addition, it is found that, for smaller and larger probability of inhibitory synapses, intermittent synchronization transition is relatively profound, while for the moderate probability of inhibitory synapses, synchronization transition seems less profound. More interestingly, it is found that as the probability of inhibitory synapses is large, regions of synchronization are upscattering.

Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling.

This paper investigates the dependence of synchronization transitions of bursting oscillations on the information transmission delay over scale-free neuronal networks with attractive and repulsive coupling. It is shown that for both types of coupling, the delay always plays a subtle role in either promoting or impairing synchronization. In particular, depending on the inherent oscillation period of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. For attractive coupling, the minima appear at every integer multiple of the average oscillation period, while for the repulsive coupling, they appear at every odd multiple of the half of the average oscillation period. The obtained results are robust to the variations of the dynamics of individual neurons, the system size, and the neuronal firing type. Hence, they can be used to characterize attractively or repulsively coupled scale-free neuronal networks with delays.

Delay-induced synchronization transition in small-world Hodgkin-Huxley neuronal networks with channel blocking

We study the evolution of spatiotemporal dynamics and synchronization transition on small-world Hodgkin-Huxley (HH) neuronal networks that are characterized with channel noises, ion channel blocking and information transmission delays. In particular, we examine the effects of delay on spatiotemporal dynamics over neuronal networks when channel blocking of potassium or sodium is involved. We show that small delays can detriment synchronization in the network due to a dynamic clustering anti-phase synchronization transition. We also show that regions of irregular and regular wave propagations related to synchronization transitions appear intermittently as the delay increases, and the delay-induced synchronization transitions manifest as well-expressed minima in the measure for spatial synchrony. In addition, we show that the fraction of sodium or potassium channels can play a key role in dynamics of neuronal networks. Furthermore, We found that the fraction of sodium and potassium channels has different impacts on spatiotemporal dynamics of neuronal networks, respectively. Our results thus provide insights that could facilitate the understanding of the joint impact of ion channel blocking and information transmission delays on the dynamical behaviors of realistic neuronal networks.

Ordering chaos and synchronization transitions by chemical delay and coupling on scale-free neuronal networks

Chemical synaptic connections are more common than electric ones in neurons, and information transmission delay is especially significant for the synapses of chemical type. In this paper, we report a phenomenon of ordering spatiotemporal chaos and synchronization transitions by the delays and coupling through chemical synapses of modified Hodgkin–Huxley (MHH) neurons on scale-free networks. As the delay τ is increased, the neurons exhibit transitions from bursting synchronization (BS) to intermittent multiple spiking synchronizations (SS). As the coupling g syn is increased, the neurons exhibit different types of firing transitions, depending on the values of τ. For a smaller τ, there are transitions from spatiotemporal chaotic bursting (SCB) to BS or SS; while for a larger τ, there are transitions from SCB to intermittent multiple SS. These findings show that the delays and coupling through chemical synapses can tame the chaotic firings and repeatedly enhance the firing synchronization of neurons, and hence could play important roles in the firing activity of the neurons on scale-free networks.

Delay-induced coherence bi-resonance-like behavior in stochastic Hodgkin-Huxley neuron networks

In this paper, we study how information transmission delays affect the spiking behavior of electrically coupled stochastic Hodgkin-Huxley (HH) neurons on Newman-Watts networks. It is found that the spiking behavior becomes the most regular at an optimal time delay, indicating the occurrence of delay-induced coherence resonance-like (CR-like) behavior. Interestingly, there are different CR-like types, depending on the membrane patch size of the neuron. For a smaller patch size, only single CR-like behavior occurs; while for a larger patch size, coherence bi-resonance-like (CBR) behavior appears. These findings show that the delay-induced CR-like behavior is closely related to the channel noise strength, and the coupled neurons may exhibit different spiking behaviors under the interplay of the channel noise and time delay. Therefore, the channel noise should be taken into account in the study of time delay-related spiking activity in stochastic HH neurons. This work provides new insight into the role of channel noise and information transmission delays in realistic neural systems.

SPATIAL COHERENCE RESONANCE IN DELAYED HODGKIN–HUXLEY NEURONAL NETWORKS

We study the phenomenon of spatial coherence resonance (SCR) on Hodgkin–Huxley (HH) neuronal networks that are characterized with information transmission delay. In particular, we examine the ability of additive Gaussian noise to optimally extract a particular spatial frequency of excitatory waves in diffusive and small-world networks on which information transmission amongst directly connected neurons is not instantaneous. On diffusively coupled HH networks, we find that for short delay lengths, there always exists an intermediate noise level by which the noise-induced spatial dynamics is maximally ordered, hence implying the possibility of SCR in the system. Importantly thereby, the noise level warranting optimally ordered excitatory waves increases linearly with the increasing delay time, suggesting that extremely long delays might nevertheless preclude the observation of SCR on diffusive networks. Moreover, we find that the small-world topology introduces another obstacle for the emergence of ordered spatial dynamics out of noise because the magnitude of SCR fades progressively as the fraction of rewired links increases, hence evidencing decoherence of noise-induced spatial dynamics on delayed small-world HH networks. Presented results thus provide insights that could facilitate the understanding of the joint impact of noise and information transmission delay on realistic neuronal networks.

Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling

We study synchronization transitions and pattern formation on small-world networks consisting of Morris–Lecar excitable neurons in dependence on the information transmission delay and the rewiring probability. In addition, networks formed via gap junctional connections and coupling via chemical synapses are considered separately. For gap-junctionally coupled networks we show that short delays can induce zigzag fronts of excitations, whereas long delays can further detriment synchronization due to a dynamic clustering anti-phase synchronization transition. For the synaptically coupled networks, on the other hand, we find that the clustering anti-phase synchronization can appear as a direct consequence of the prolongation of information transmission delay, without being accompanied by zigzag excitatory fronts. Irrespective of the coupling type, however, we show that an appropriate small-world topology can always restore synchronized activity if only the information transmission delays are short or moderate at most. Long information transmission delays always evoke anti-phase synchronization and clustering, in which case the fine-tuning of the network topology fails to restore the synchronization of neuronal activity.

Consensus in networks under transmission delays and the normalized Laplacian

We study discrete and continuous time consensus problems on directed and weighted networks in the presence of time delays. We focus on information transmission delays, as opposed to information processing delays, so that each node of the network compares its current state to the past states of its neighbors. Furthermore, we allow both fixed and distributed time delays. The connection structure of the network is described by a normalized Laplacian matrix. We show that consensus is achieved if and only if the underlying graph contains a spanning tree. Furthermore, this statement holds independently of the value of the delay, in contrast to the case of processing delays. We also calculate the consensus value and show that, unlike the case of processing delays, the consensus value is determined not just by the initial states of the nodes at time zero, but also on their past history over an interval of time.