AntiDisturbance of ScaleFree Spiking Neural Network against Impulse Noise
Abstract
:1. Introduction
2. Construction of SFSNN
2.1. Generation of a ScaleFree Network
 (1)
 Scalefree property
 (2)
 Clustering coefficient
2.2. Izhikevich Neuron Model
2.3. Synaptic Plasticity Model
2.4. Construction Process of the SFSNN
Algorithm 1 The construction algorithm of the SFSNN 
Input: Adjacency matrix of the scalefree network at $\mathit{P}=0.3$ Output: The highclustering SFSNN

3. AntiDisturbance of the SFSNN
3.1. External Disturbance and AntiDisturbance Indexes
 Impulse noiseImpulse noise is an irregular discontinuous signal composed of pulse spikes, which is characterized by short duration, large amplitude and burst. It can be described as follows:$$s\left(t\right)=\left(\right)open="\{"\; close>\begin{array}{c}{A}_{s},t\in [{T}_{0},{T}_{0}+T]\hfill \\ 0,else\hfill \end{array}$$
 The indexes of antidisturbance
 (1)
 The relative change rate of the firing rateThe firing rate of a neuron reflects the frequency of action potentials per unit of time in a neuron. The relative change rate of the firing rate $\delta $ can characterize the change degree of the neuronal firing rate before and after disturbance, which is defined as follows:$$\delta =\frac{\left(\right)}{{f}_{j}}{f}_{i}$$
 (2)
 The correlation between membrane potentialThe correlation between membrane potential $\rho $ reflects the degree of similarity between the membrane potentials of the neurons before and after disturbance, which is defined as follows:$$\rho \left(\tau \right)=\frac{{\displaystyle \sum _{t={t}_{1}}^{{t}_{2}\tau +1}}{x}_{i}\left(t\right){x}_{j}(t+\tau )}{\sqrt{{\displaystyle \sum _{t={t}_{1}}^{{t}_{2}\tau +1}}{x}_{i}^{2}\left(t\right){\displaystyle \sum _{t={t}_{1}}^{{t}_{2}\tau +1}}{x}_{j}^{2}(t+\tau )}}$$
3.2. AntiDisturbance Ability of the SFSNN
3.3. Comparison of AntiDisturbance Ability
 (1)
 Calculate the difference w between two samples. If w is a positive number, denote it as a positive sign; otherwise, w is a negative number, denoted it as a negative sign.
 (2)
 Calculate the corresponding order by sorting the absolute value of w.
 (3)
 Calculate the sum order of the positive and negative signs w, denoted as ${w}^{+}$ and ${w}^{}$, respectively.
4. Discussion
4.1. Firing Rate
4.2. Synaptic Weight
4.3. Relevance between the Synaptic Plasticity and the AntiDisturbance Ability
4.3.1. Pearson Correlation Coefficient and tTest
4.3.2. Evolution Process of the AntiDisturbance Ability
4.3.3. Relevance Analysis
4.4. Effect of Network Topology on the AntiDisturbance Ability
4.4.1. Weighted Clustering Coefficient
4.4.2. Evolution Process of the Weighted Clustering Coefficient
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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p  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.0 

$\gamma $  1.55  1.82  2.15  2.41  2.51  2.76  2.86  2.87  2.98  3.18 
C  0.7028  0.6236  0.5001  0.4707  0.4180  0.3884  0.3133  0.2524  0.1889  0.1643 
Types of SFSNN  HighClustering  LowClustering 

$\delta $  −0.915 **  −0.988 ** 
$\rho $  −0.970 **  −0.963 ** 
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Guo, L.; Guo, M.; Wu, Y.; Xu, G. AntiDisturbance of ScaleFree Spiking Neural Network against Impulse Noise. Brain Sci. 2023, 13, 837. https://doi.org/10.3390/brainsci13050837
Guo L, Guo M, Wu Y, Xu G. AntiDisturbance of ScaleFree Spiking Neural Network against Impulse Noise. Brain Sciences. 2023; 13(5):837. https://doi.org/10.3390/brainsci13050837
Chicago/Turabian StyleGuo, Lei, Minxin Guo, Youxi Wu, and Guizhi Xu. 2023. "AntiDisturbance of ScaleFree Spiking Neural Network against Impulse Noise" Brain Sciences 13, no. 5: 837. https://doi.org/10.3390/brainsci13050837