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.
Inhibitory coupled bursting Hindmarsh-Rose neurons are considered as constitutive units of the Macaque corti- cal 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 synchro- nization 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 transi- tions 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.
The stochastic resonance in paced time-delayed scale-free FitzHugh--Nagumo （FHN） neuronal networks is investigated. We show that an intermediate intensity of additive noise is able to optimally assist the pacemaker in imposing its rhythm on the whole ensemble. Furthermore, we reveal that appropriately tuned delays can induce stochastic multiresonances, appearing at every integer multiple of the pacemaker＇s oscillation period. We conclude that fine-tuned delay lengths and locally acting pacemakers are vital for ensuring optimal conditions for stochastic resonance on complex neuronal networks.
