Effects of coupling strength and network topology on signal detection in small-world neuronal networks

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.

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

International Journal of Neural Systems ◽

10.1142/s0129065711002924 ◽

2011 ◽

Vol 21 (05) ◽

pp. 415-425 ◽

Cited By ~ 23

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.

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The optimal synchronizability of complex networks with saturated coupling strength

International Journal of Modern Physics C ◽

10.1142/s0129183120501399 ◽

2020 ◽

Vol 31 (10) ◽

pp. 2050139

Author(s):

Chen Huang ◽

Xinbiao Lu ◽

Jun Zhou ◽

Buzhi Qin

Keyword(s):

Genetic Algorithm ◽

Global Optimization ◽

Network Topology ◽

Coupling Strength ◽

Small World ◽

Pso Algorithm ◽

Small World Network ◽

Swarm Optimization ◽

Edge Betweenness ◽

Simulation Results

For networks with fixed network topology, when the total coupling strength between nodes is limited and the coupling strength between nodes is saturated, the global optimization algorithms including genetic algorithm (GA) and particle swarm optimization (PSO) algorithm are used to adjust the coupling strength between nodes to improve the synchronizability of the network, respectively. Simulation results show that in WS small-world network, when the edge betweenness centrality of the edge is large, the coupling strength of the edge after optimization is greater. Furthermore, compared with GA, PSO has better performance.

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CELLULAR NEURAL NETWORKS CAN MIMIC SMALL-WORLD NETWORKS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127499001541 ◽

1999 ◽

Vol 09 (10) ◽

pp. 2105-2126 ◽

Cited By ~ 6

Author(s):

TAO YANG ◽

LEON O. CHUA

Keyword(s):

Neural Networks ◽

Coupling Strength ◽

Initial Conditions ◽

Computing Time ◽

Small World ◽

Cellular Neural Networks ◽

Clustering Coefficient ◽

High Survival ◽

Game Of Life ◽

Hole Detection

Small-world phenomenon can occur in coupled dynamical systems which are highly clustered at a local level and yet strongly coupled at the global level. We show that cellular neural networks (CNN's) can exhibit "small-world phenomenon". We generalize the "characteristic path length" from previous works on "small-world phenomenon" into a "characteristic coupling strength" for measuring the average coupling strength of the outputs of CNN's. We also provide a simplified algorithm for calculating the "characteristic coupling strength" with a reasonable amount of computing time. We define a "clustering coefficient" and show how it can be calculated by a horizontal "hole detection" CNN, followed by a vertical "hole detection" CNN. Evolutions of the game-of-life CNN with different initial conditions are used to illustrate the emergence of a "small-world phenomenon". Our results show that the well-known game-of-life CNN is not a small-world network. However, generalized CNN life games whose individuals have strong mobility and high survival rate can exhibit small-world phenomenon in a robust way. Our simulations confirm the conjecture that a population with a strong mobility is more likely to qualify as a small world. CNN games whose individuals have weak mobility can also exhibit a small-world phenomenon under a proper choice of initial conditions. However, the resulting small worlds depend strongly on the initial conditions, and are therefore not robust.

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Effects of Time Delay on Burst Synchronization Transition of Neuronal Networks

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127418501432 ◽

2018 ◽

Vol 28 (12) ◽

pp. 1850143 ◽

Cited By ~ 2

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.

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Broad-scale small-world network topology induces optimal synchronization of flexible oscillators

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2014.08.008 ◽

2014 ◽

Vol 69 ◽

pp. 14-21 ◽

Cited By ~ 4

Author(s):

Rene Markovič ◽

Marko Gosak ◽

Marko Marhl

Keyword(s):

Network Topology ◽

Small World ◽

Small World Network ◽

Broad Scale

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Effects of distance-dependent delay on small-world neuronal networks

Physical Review E ◽

10.1103/physreve.93.042417 ◽

2016 ◽

Vol 93 (4) ◽

Cited By ~ 9

Author(s):

Jinjie Zhu ◽

Zhen Chen ◽

Xianbin Liu

Keyword(s):

Neuronal Networks ◽

Small World

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Modeling and Simulation for Complex Network Based Military System-of-Systems (SoS)

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.145.224 ◽

2011 ◽

Vol 145 ◽

pp. 224-228 ◽

Cited By ~ 2

Author(s):

Xiao Song ◽

Bing Cheng Liu ◽

Guang Hong Gong

Keyword(s):

Modeling And Simulation ◽

Complex Network ◽

Network Topology ◽

Network Theory ◽

Small World ◽

System Of Systems ◽

Statistical Parameters ◽

Complex Network Theory ◽

Scale Free ◽

Topology Model

Military SoS increasingly shows its relation of complex network. According to complex network theory, we construct a SoS network topology model for network warfare simulation. Analyzing statistical parameters of the model, it is concluded that the topology model has small-world, high-aggregation and scale-free properties. Based on this model we mainly simulate and analyze vulnerability of the network. And this provides basis for analysis of the robustness and vulnerability of real battle SoS network.

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