The evolution to global burst synchronization in a modular neuronal network

2016 ◽  
Vol 30 (14) ◽  
pp. 1650210 ◽  
Author(s):  
Xiaoli Yang ◽  
Manman Wang
Keyword(s):  
Neuronal Network ◽  
Coupling Strength ◽  
Numerical Results ◽  
Network Behavior ◽  
Modular Network ◽  
Scale Free ◽  
Macroscopic Property ◽  
Coupling Strengths ◽  
Burst Synchronization ◽  
Modular Neuronal Network

In this paper, we investigated the development of global burst synchronization in a modular neuronal network at the mesoscale level. The modular network consists of some subnetworks, each of them presenting a scale-free property. Numerical results have demonstrated that, upon increasing the coupling strength, all neurons in the modular network initially burst in a desynchronous pattern; then the burst synchronization within each subnetwork is followed at the mesoscale; finally, the global burst synchronization at the macroscale is formed by the bursting activities on each subnetwork moving forward in harmony. This implies the network behavior possesses two distinct mesoscopic and macroscopic properties for some coupling strengths, i.e. the mesoscopic dynamics of burst synchronization on subnetworks is different from the macroscopic property of desynchronous activity on the whole network. It is also found that global burst synchronization can be promoted by large interconnection probability and hindered by small interconnection probability.

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.

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.

scholarly journals Cluster Burst Synchronization in A Scale-Free Network of Inhibitory Bursting Neurons

2018 ◽  
Author(s):  
Sang-Yoon Kim ◽  
Woochang Lim
Keyword(s):  
Coupling Strength ◽  
Synaptic Inhibition ◽  
Stochastic Noise ◽  
Scale Free Network ◽  
Scale Free ◽  
Bursting Neurons ◽  
Raster Plot ◽  
Free Network ◽  
Burst Synchronization

We consider a scale-free network of inhibitory Hindmarsh-Rose (HR) bursting neurons, and investigate coupling-induced cluster burst synchronization by varying the average coupling strength J0. For sufficiently small J0, non-cluster desynchronized states exist. However, when passing a critical point , the whole population is segregated into 3 clusters via a constructive role of synaptic inhibition to stimulate dynamical clustering between individual burstings, and thus 3-cluster desynchronized states appear. As J0 is further increased and passes a lower threshold , a transition to 3-cluster burst synchronization occurs due to another constructive role of synaptic inhibition to favor population synchronization. In this case, HR neurons in each cluster exhibit burst synchronization. However, as J0 passes an intermediate threshold , HR neurons begin to make intermittent hoppings between the 3 clusters. Due to the intermittent intercluster hoppings, the 3 clusters are integrated into a single one. In spite of break-up of the 3 clusters, (non-cluster) burst synchronization persists in the whole population, which is well visualized in the raster plot of burst onset times where bursting stripes (composed of burst onset times and indicating burst synchronization) appear successively. With further increase in J0, intercluster hoppings are intensified, and bursting stripes also become smeared more and more due to a destructive role of synaptic inhibition to spoil the burst synchronization. Eventually, when passing a higher threshold a transition to desynchronization occurs via complete overlap between the bursting stripes. Finally, we also investigate the effects of stochastic noise on both 3-cluster burst synchronization and intercluster hoppings.

IN-PHASE BURST SYNCHRONIZATION AND RHYTHM DYNAMICS OF COMPLEX NEURONAL NETWORKS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250101 ◽  
Author(s):  
XIA SHI ◽  
QISHAO LU ◽  
HAIXIA WANG
Keyword(s):  
Neuronal Network ◽  
Network Topology ◽  
Coupling Strength ◽  
Neuronal Networks ◽  
Quantitative Characteristic ◽  
Coupling Scheme ◽  
Average Width ◽  
Bursting Neurons ◽  
Burst Synchronization ◽  
Width Factor

In-phase burst synchronization, spatiotemporal order and rhythm dynamics of a complex neuronal network with electrical or chemically excitatory synapses are studied in this paper. A quantitative characteristic, the width factor, is introduced to describe the rhythm dynamics of an individual neuron, and the average width factor is used to characterize the rhythm dynamics of a neural network. The in-phase burst synchronization is studied in terms of the burst phase order parameter. We also study the effects of the coupling schemes, the intrinsic neuronal property and the network topology on the rhythm dynamics of the network. It is found that the neuronal network with electrical coupling is easier to realize the in-phase burst synchronization than that with the chemically excitatory coupling. The bursting type of short bursting neuronal networks is unchanged for different coupling schemes with the coupling strength increasing. Moreover, the short bursting type is robust both to the coupling strength and the coupling scheme. As for the network topology, more links can only change the bursting type of long bursting neurons, but short bursting neurons are robust to the link numbers.

EVOLUTION OF ATOM-FIELD PROBABILITY IN A COUPLED CAVITY SYSTEM

2013 ◽  
Vol 22 (03) ◽  
pp. 1350029
Author(s):  
K. V. PRIYESH ◽  
RAMESH BABU THAYYULLATHIL
Keyword(s):  
Coupling Strength ◽  
Probability Amplitude ◽  
Field Coupling ◽  
Level Atom ◽  
Cavity System ◽  
Coupling Strengths ◽  
Field Excitation ◽  
Excitation Probability ◽  
Hopping Strength ◽  
Coupled Cavity

In this paper we have investigated the dynamics of two cavities each with a two-level atom, coupled together with photon hopping. The coupled cavity system is studied in single excitation subspace and the evolution of the atom (field) states probabilities are obtained analytically. The probability amplitude of states executes oscillations with different modes and amplitudes, determined by the coupling strengths. The evolution is examined in detail for different atom field coupling strength, g and field–field hopping strength, A. It is noticed that the exact atomic probability amplitude transfer occurs when g ≪ A with minimal field excitation probability and the period of probability transfer is calculated. In the limit g ≫ A there exists periodic exchange of probability between atom and field inside each cavity and also between cavity 1 and cavity 2. Periodicity of each exchange in this limit also obtained.

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