# Dynamic Pathway Selection Mechanisms of Brain Networks
## 3 Results
### Two Motif Models  
By constructing the motif model of two neurons based on dynamic synapse, the synchronization phenomenon and effective link in the network are studied. The neuron node is driven by external stimulus and its amplitude intensity is \(a=1\). The signal frequency is \(f=11\) Hz. The discharge sequence between two neurons in different coupling connection states and the statistical distribution of two neurons in the connection state are shown in Figures 2 and 3, respectively.  
Figure 3: PSF boxplots for the different coupling states.  
Figure 2: Two neuronal discharge sequences (**a**) Neurons A and B are unidirectional coupling; (**b**) Neurons A and B are dual coupling.).  
Figure 2 shows the discharge sequence between two neurons with different coupling connections. Figure 2a shows that, in the unidirectional coupling state, such as the structure of Figure 1(a-1), discharge sequence between neurons demonstrates a lack of consistency, and the synchronization activity between neuron \(A\) and neuron \(B\) is weak. This is because there is only one-way action between neurons and there is no feedback link. When the neurons are in the state of two-way coupling connection (i.e., feedback link exists), as shown in Figure 1(a-2) structure and the discharge sequence shown in Figure 2b, it can be seen that the discharge sequences between neurons are highly consistent and the pulse sequences coincide at a fixed time. This phenomenon is called isochronous synchronization.  
Figure 3 is a box-line plot that quantitatively portrays the values of the \(PSF\) taken under different coupling connections. The upper and lower limits of the bins each indicate the upper and lower quartiles, the entire box indicates the dispersion of the \(PSF\) and the line in the middle indicates the median of the dataset. Through running the experimental data 100 times, Figure 3 quantitatively describe the values under different coupling connections. For the dual coupled motif model, the \(PSF\) exponent is higher, i.e., it shows that it is more sensitive to the phase information carried by the input information. For the single coupling model, the \(PSF\) value is around 0.28. The smaller \(PSF\) value indicates that the phase carried by the input information has less impact on it under this structure, i.e., the synchronization of the nodes is less affected when the stimulus information changes the carried phase, which, in turn, cannot regulate the effective links in the network.  
In the brain network, the \(PSF\) is affected not only by the phase shift of the stimulus, but also by the time delay. Therefore, this study considers the transmission delay between transmission paths and describes the effect of delay on the \(PSF\). The simulation is shown in Figure 4.  
Figure 4 represents the \(PSF\) effect under the time delay scale of \([0,\ 200]\). From Figure 4, it is seen that the \(PSF\) value under single coupling fluctuates around 0.43 and does not change significantly with the increase in time delay, indicating that the phase information carried by the stimulus phase has less ability to regulate under the single coupling structure under the influence of time delay, and its coherence value \(PC\) is more stable. In bidirectional coupling, the \(PSF\) value has a strong fluctuation between \([0.1,\ 0.52]\). With the increase in time delay, the \(PSF\) value appears to show a trend of in-phase and inverse-to-phase changes, which shows that the synchronization of neural nodes can be regulated in-phase or inverse-to by means of time delay [17; 18; 19]. Therefore, exploring the effect of time delay on \(PSF\) between coupled nodes is important to investigating the relationship between stimulus information phase shift and the selection mechanism of network paths.  
Figure 4: Effect of time delay of two motif model on PSF.