Burst Synchronization in a Small-World Neuronal Network with Coupling Delays

2010 ◽  
pp. 283-288
Author(s):  
Jiaoyan Wang ◽  
Qishao Lu ◽  
Fang Han ◽  
Zhuoqin Yang
Keyword(s):  
Neuronal Network ◽  
Small World ◽  
Burst Synchronization

Synchronization and rhythm dynamics of a neuronal network consisting of mixed bursting neurons with hybrid synapses

2016 ◽  
Vol 30 (16) ◽  
pp. 1650091 ◽  
Author(s):  
Xia Shi ◽  
Wenqi Xi
Keyword(s):  
Neuronal Network ◽  
Coupling Strength ◽  
Small World ◽  
Inhibitory Synapses ◽  
Small World Network ◽  
Average Width ◽  
Bursting Neurons ◽  
Burst Synchronization ◽  
Chemical Synapses ◽  
Width Factor

In this paper, burst synchronization and rhythm dynamics of a small-world neuronal network consisting of mixed bursting types of neurons coupled via inhibitory–excitatory chemical synapses are explored. Two quantities, the synchronization parameter and average width factor, are used to characterize the synchronization degree and rhythm dynamics of the neuronal network. Numerical results show that the percentage of the inhibitory synapses in the network is the major factor for we get a similarly bell-shaped dependence of synchronization on it, and the decrease of the average width factor of the network. We also find that not only the value of the coupling strength can promote the synchronization degree, but the probability of random edges adding to the small-world network also can. The ratio of the long bursting neurons has little effect on the burst synchronization and rhythm dynamics of the network.

Chaotic burst synchronization in a two-small-world-layer neuronal network

2015 ◽  
Vol 26 (05) ◽  
pp. 1550051 ◽  
Author(s):  
Yanhong Zheng ◽  
Haixia Wang
Keyword(s):  
Neuronal Network ◽  
Coupling Strength ◽  
Small World ◽  
Interlayer Coupling ◽  
The Other ◽  
Spatiotemporal Pattern ◽  
Small Noise ◽  
Irregular Pattern ◽  
Burst Synchronization ◽  
Chaotic Burst

Chaotic burst synchronization in a two-small-world-layer neuronal network is studied in this paper. For a neuronal network coupled by two single-small-world-layer networks with link probability differences between layers, the two-layer network can achieve synchrony as the interlayer coupling strength increases. When chaotic layer network is coupled with chaotic-burst-synchronization layer network, the latter is dominant at small interlayer coupling strength, so it can make the layer with the irregular pattern show some regular and also exhibit the same pattern with the other layer. However, when chaotic layer is coupled with firing synchronization layer, the ordered layer is dominated by a disordered one with the interlayer coupling strength increasing. When the interlayer coupling strength is large enough, both networks are chaotic burst synchronization. Therefore, the synchronous states strongly depend on the interlayer coupling strength and the link probability. Moreover, the spatiotemporal pattern synchronization between the networks is robust to small noise.

Effects of Time Delay on Burst Synchronization Transition of Neuronal Networks

2018 ◽  
Vol 28 (12) ◽  
pp. 1850143 ◽  
Author(s):  
Xiaojuan Sun ◽  
Tianshu Xue
Keyword(s):  
Time Delay ◽  
Neuronal Network ◽  
Coupling Strength ◽  
Neuronal Networks ◽  
The Other ◽  
Electrical Synapses ◽  
Synchronization Transition ◽  
Burst Synchronization ◽  
Chemical Synapses ◽  
Bursting Activity

In this paper, we focus on investigating the effects of time delay on burst synchronization transitions of a neuronal network which is locally modeled by Hindmarsh–Rose neurons. Here, neurons inside the neuronal network are connected through electrical synapses or chemical synapses. With the numerical results, it is revealed that burst synchronization transitions of both electrically and chemically coupled neuronal networks could be induced by time delay just when the coupling strength is large enough. Meanwhile, it is found that, in electrically and excitatory chemically coupled neuronal networks, burst synchronization transitions are observed through change of spiking number per burst when coupling strength is large enough; while in inhibitory chemically coupled neuronal network, burst synchronization transitions are observed for large enough coupling strength through changing fold-Hopf bursting activity to fold-homoclinic bursting activity and vice versa. Namely, two types of burst synchronization transitions are observed. One type of burst synchronization transitions occurs through change of spiking numbers per burst and the other type of burst synchronization transition occurs through change of bursting types.

scholarly journals Delay-induced synchronization transition in a small-world neuronal network of FitzHugh–Nagumo neurons subjected to sine-Wiener bounded noise

2019 ◽  
Vol 33 (08) ◽  
pp. 1950053 ◽  
Author(s):  
Yuangen Yao ◽  
Ming Yi ◽  
Dejia Hou
Keyword(s):  
Neuronal Network ◽  
Correlation Time ◽  
Small World ◽  
Nearest Neighbors ◽  
Spatiotemporal Patterns ◽  
Small World Network ◽  
Bounded Noise ◽  
Future Studies ◽  
Synchronization Transition ◽  
Brain Functions

Noise and delay are ubiquitous in brain and they have significant effects on neuronal network synchronization and even brain functions. Based on a small-world neuronal network of delayed FitzHugh–Nagumo (FHN) neurons subjected to sine-Wiener (SW) bounded noise, the effects of delay and SW noise on synchronization and synchronization transition are numerically investigated by calculating a synchronization measure R and plotting spatiotemporal patterns. The phenomenon of delay-induced synchronization transition is observed as delay [Formula: see text] is increased. And large self-correlation time and strength of SW noise can increase the number of delay-induced synchronization transition. In addition, delay-induced synchronization transition is robust against the change of topology structure of neuronal network and this phenomenon becomes much easier to see for small nearest neighbors k in the small-world network. Since synchronization transition may imply functional switch, our results may have important implications, and inspire future studies.

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