Influence of synaptic interaction on firing synchronization and spike death in excitatory neuronal networks

Synchronous slowing down in coupled logistic maps via random network topology

The speed and paths of synchronization play a key role in the function of a system, which has not received enough attention up to now. In this work, we study the synchronization process of coupled logistic maps that reveals the common features of low-dimensional dissipative systems. A slowing down of synchronization process is observed, which is a novel phenomenon. The result shows that there are two typical kinds of transient process before the system reaches complete synchronization, which is demonstrated by both the coupled multiple-period maps and the coupled multiple-band chaotic maps. When the coupling is weak, the evolution of the system is governed mainly by the local dynamic, i.e., the node states are attracted by the stable orbits or chaotic attractors of the single map and evolve toward the synchronized orbit in a less coherent way. When the coupling is strong, the node states evolve in a high coherent way toward the stable orbit on the synchronized manifold, where the collective dynamics dominates the evolution. In a mediate coupling strength, the interplay between the two paths is responsible for the slowing down. The existence of different synchronization paths is also proven by the finite-time Lyapunov exponent and its distribution.

Effect of autaptic activity on the response of a Hodgkin-Huxley neuron

An autapse is a special synapse that connects a neuron to itself. In this study, we investigated the effect of an autapse on the responses of a Hodgkin-Huxley neuron to different forms of external stimuli. When the neuron was subjected to a DC stimulus, the firing frequencies and the interspike interval distributions of the output spike trains showed periodic behaviors as the autaptic delay time increased. When the input was a synaptic pulse-like train with random interspike intervals, we observed low-pass and band-pass filtering behaviors. Moreover, the region over which the output ISIs are distributed and the mean firing frequency display periodic behaviors with increasing autaptic delay time. When specific autaptic parameters were chosen, most of the input ISIs could be filtered, and the response spike trains were nearly regular, even with a highly random input. The background mechanism of these observed dynamics has been analyzed based on the phase response curve method. We also found that the information entropy of the output spike train could be modified by the autapse. These results also suggest that the autapse can serve as a regulator of information response in the nervous system.

Experimental study of firing death in a network of chaotic FitzHugh-Nagumo neurons

The FitzHugh-Nagumo neurons driven by a periodic forcing undergo a period-doubling route to chaos and a transition to mixed-mode oscillations. When coupled, their dynamics tend to be synchronized. We show that the chaotically spiking neurons change their internal dynamics to subthreshold oscillations, the phenomenon referred to as firing death. These dynamical changes are observed below the critical coupling strength at which the transition to full chaotic synchronization occurs. Moreover, we find various dynamical regimes in the subthreshold oscillations, namely, regular, quasiperiodic, and chaotic states. We show numerically that these dynamical states may coexist with large-amplitude spiking regimes and that this coexistence is characterized by riddled basins of attraction. The reported results are obtained for neurons implemented in the electronic circuits as well as for the model equations. Finally, we comment on the possible scenarios where the coupling-induced firing death could play an important role in biological systems.

Complexity versus modularity and heterogeneity in oscillatory networks: combining segregation and integration in neural systems

Normal functioning in many realistic complex dynamical systems, such as neural networks, requires coherence and synchronization for collective actions of network components. However, strong synchronization of the whole network is often related to pathological situations. A regime in between enabling both segregation in subsystems and integration as a whole is thus desirable. Here, we characterize this regime by complexity of synchronization patterns and study its relationship to heterogeneous and modular architecture in complex network of oscillators. We show that these networks possess a broad range of high complexity associated with the formation of dynamical clusters and the coordination between the clusters. In realistic networks of C. elegans and cat cortex, the complexity is reduced when the original network is rewired in various ways, reflecting that the neural systems are organized to provide a combination of segregation and integration with the coexistence of various complex network features, especially modularity and heterogeneity. Our work can stimulate further studies on structure-function relationships in neural systems through the inquiry of the specific functional roles of the intermediate dynamical regime.

Propagation of firing rate by synchronization and coherence of firing pattern in a feed-forward multilayer neural network

When neurons in layer 1 fire irregularly under stochastic noise, it is found synchronous firings can develop gradually in latter layers within a feed-forward multilayer neural network, which is consistent with experimental findings. The underlying mechanism of propagation of firing rate is explored, then rate encoding realized by synchronization is clarified. Furthermore, the effects of connection probability between nearest layers, stochastic noise, and ratio of inhibitory connections to total connection on (i) propagation of firing rate by synchronization and (ii) coherence of firing pattern are investigated, respectively. It is observed that (i) there is a threshold for connection probability, beyond which firing rate of each layer can propagate successfully through the whole network by synchronization. The dependence of firing rate on layer index is very different for different connection probability. In addition, larger the connection probability is, more rapidly the synchrony is built up. (ii) Increasing intensity of stochastic noise enhances firing rate in output layer. Stochastic noise plays a constructive role in improving synchrony by causing the synchronization more quickly. (iii) The inhibitory connection offsets excitatory input therefore reduces firing rate and synchrony. As layer index increases, coherence measure goes through a peak, i.e., the coherence of firing pattern is the worst at certain a layer. With increasing the ratio of inhibitory connections, the variability of firing train is enhanced, exhibiting destructive role of inhibitory connections on coherence of firing pattern.