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.

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.

SYNCHRONIZATION IN A RING OF UNIDIRECTIONALLY COUPLED FITZHUGH–NAGUMO NEURONS

2014 ◽  
Vol 07 (01) ◽  
pp. 1450009 ◽  
Author(s):  
ANINDITA BHATTACHARJEE ◽  
M. K. DAS ◽  
SUBHENDU GHOSH
Keyword(s):  
Time Delay ◽  
Coupling Strength ◽  
Delayed Feedback ◽  
Feedback Gain ◽  
Model Parameters ◽  
Constant Input ◽  
Synchronization Phenomenon ◽  
Error Dynamics ◽  
Chemical Synapses

Synchronization behavior of an ensemble of unidirectionally coupled neurons with a constant input is investigated. Chemical synapses are considered for coupling. Each neuron is also considered to be exposed to a self-delayed feedback. The synchronization phenomenon is analyzed by the error dynamics of the response trajectories of the system. The effect of various model parameters e.g. coupling strength, feedback gain and time delay, on synchronization is also investigated and a measure of synchrony is computed in each cases. It is shown that the synchronization is not only achieved by increasing the coupling strength, the system also required to have a suitable feedback gain and time delay for synchrony. Robustness of the parameters for synchrony is verified for larger systems.

scholarly journals Synchronization of the neurons coupled with sequential developing electrical and chemical synapses

2021 ◽  
Vol 19 (2) ◽  
pp. 1877-1890
Author(s):  
Zhen Wang ◽  
◽  
Ramesh Ramamoorthy ◽  
Xiaojian Xi ◽  
Hamidreza Namazi ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Transition Period ◽  
Brain Regions ◽  
Synchronization Error ◽  
Electrical Synapses ◽  
Burst Synchronization ◽  
Chemical Synapses ◽  
Over Time ◽  
Sequential Formation ◽  
Modeling Study

<abstract> <p>There is some evidence representing the sequential formation and elimination of electrical and chemical synapses in particular brain regions. Relying on this feature, this paper presents a purely mathematical modeling study on the synchronization among neurons connected by transient electrical synapses transformed to chemical synapses over time. This deletion and development of synapses are considered consecutive. The results represent that the transient synapses lead to burst synchronization of the neurons while the neurons are resting when both synapses exist constantly. The period of the transitions and also the time of presence of electrical synapses to chemical ones are effective on the synchronization. The larger synchronization error is obtained by increasing the transition period and the time of chemical synapses' existence.</p> </abstract>

scholarly journals The Synchronization and Synchronization Transition of Coupled Fractional-order Neuronal Networks

2021 ◽  
Author(s):  
Xin Yang ◽  
GuangJun Zhang ◽  
XueRen Li ◽  
Dong Wang
Keyword(s):  
Electromagnetic Radiation ◽  
Fractional Order ◽  
Neuronal Network ◽  
Neuronal Networks ◽  
Phase Synchronization ◽  
Chaotic Synchronization ◽  
Feedback Gain ◽  
Synchronization Transition ◽  
Conductance Parameter ◽  
Small Change

Abstract Different from the previous researches on the synchronization and synchronization transition of neuronal networks constructed by integer-order neuronal models, the synchronization and synchronization transition of fractional-order neuronal network are investigated in this paper. The fractional-order ring neuronal network constructed by fractional-order HindmarshRose (HR) neuronal models without electromagnetic radiation are proposed, and it’s synchronization behaviors are investigated numerically. The synchronization behaviors of two coupled fractional-order neuronal models and ring neuronal network under electromagnetic radiation are studied numerically. By research results, several novel phenomena and conclusions can be drawn. First, for the fractional-order HR model’s ring neuronal network without electromagnetic radiation, if the fractional-order q is changed, the threshold of the coupling strength when the network is in perfect synchronization will change. Furthermore, the change of fractional-order can induce the transition of periodic synchronization and chaotic synchronization. Second, for the two coupled neurons under electromagnetic radiation, the synchronization degree is influenced by fractional-order and the feedback gain parameter k1 . In addition, the fractional-order and parameter k1 can induce the synchronization transition of bursting synchronization, perfect synchronization and phase synchronization. For the perfect synchronization, the synchronization transition of chaotic synchronization and periodic synchronization induced by q and parameter k1 is also observed. Especially, When the fractionalorder is small, like 0.6, the synchronization behavior will be more complex. Third, for the ring neuronal network under electromagnetic radiation, with the change of memory-conductance parameter β, parameter k1 and fractional-order q of electromagnetic radiation, the synchronization behaviors are different. When β > 0.02 , the synchronization will be strengthened with the decreasing of fractional-order. The parameter k1 can induce the synchronization transition of perfect periodic10 synchronization, perfect periodic-7 synchronization, perfect periodic-5 synchronization and perfect periodic4 synchronization. It is hard for the system to synchronize and q has little effect on the synchronization when −0.06 < β < 0.02 . When β < −0.06 , the network moves directly from asynchronization to perfect synchronization, and the synchronization factor goes from 0.1 to 1 with the small change of fractional-order. Larger the factional-order is, larger the range of synchronization is. The synchronization degree increases with the increasing of k1.

EXCITEMENT AND SYNCHRONIZATION OF SMALL-WORLD NEURONAL NETWORKS WITH SHORT-TERM SYNAPTIC PLASTICITY

2011 ◽  
Vol 21 (05) ◽  
pp. 415-425 ◽  
Author(s):  
FANG HAN ◽  
MARIAN WIERCIGROCH ◽  
JIAN-AN FANG ◽  
ZHIJIE WANG
Keyword(s):  
Synaptic Plasticity ◽  
Neuronal Network ◽  
Coupling Strength ◽  
Neuronal Networks ◽  
Learning Rule ◽  
Small World ◽  
Learning Rate ◽  
Short Term ◽  
Synaptic Learning

Excitement and synchronization of electrically and chemically coupled Newman-Watts (NW) small-world neuronal networks with a short-term synaptic plasticity described by a modified Oja learning rule are investigated. For each type of neuronal network, the variation properties of synaptic weights are examined first. Then the effects of the learning rate, the coupling strength and the shortcut-adding probability on excitement and synchronization of the neuronal network are studied. It is shown that the synaptic learning suppresses the over-excitement, helps synchronization for the electrically coupled network but impairs synchronization for the chemically coupled one. Both the introduction of shortcuts and the increase of the coupling strength improve synchronization and they are helpful in increasing the excitement for the chemically coupled network, but have little effect on the excitement of the electrically coupled one.

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.

The Combined Effect of Dynamic Chemical and Electrical Synapses in Time-Delay-Induced Phase-Transition to Synchrony in Coupled Bursting Neurons

2014 ◽  
Vol 24 (05) ◽  
pp. 1450069 ◽  
Author(s):  
E. B. Megam Ngouonkadi ◽  
Hilaire B. Fotsin ◽  
P. H. Louodop Fotso
Keyword(s):  
Phase Transition ◽  
Time Delay ◽  
Nonlinear Oscillators ◽  
Combined Effect ◽  
Electrical Synapses ◽  
Bursting Neurons ◽  
Coupled Nonlinear Oscillators ◽  
Binding Time ◽  
Chemical Synapses ◽  
Synaptic Parameters

In this paper, we study the combined effect of dynamic chemical and electrical synapses in time-delay-induced phase-transition to synchrony in coupled bursting neurons. Time-delay in coupled nonlinear oscillators or in a network of coupled nonlinear oscillators has been found to be responsible for striking dynamical behaviors such as phase-flip-transitions. These phenomena lead to synchrony or out of synchrony in different oscillators of the system. Here, we show that synaptic parameters, more precisely the neurotransmitters binding time constant influences the phase-flip-transitions of the system. We discuss how the system goes to the phase-flip-transitions when both electrical and dynamic chemical synapses are taken into account. The fourth-order Hindmarsh–Rose neuronal oscillator is considered here for the study of these transitions. A discussion on the importance of these results in brain researches is given, particularly to understand the collective dynamics of bursting neurons.

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