# Dynamic Pathway Selection Mechanisms of Brain Networks
## 3 Results
### Three Motif Models  
In the previous section, the synchronization status of different structural links under the two motif models is analyzed, and it is concluded that the connection structure and transmission delay have influence on the synchronization characteristics. Because the structure of the three motif models is changeable, but their essence is the extension of the two motif models, the analysis of the three motif models in Figure 1b mainly considers the synchronization state between the links of the motif model and the effective links when the structural links are missing. Therefore, we next focus on the motif model of Figure 1(b-2,b-3) in order to analyze the synchronization state and effective link under this link. Figure 1(b-2) structure is a connection model in which neuron \(C\) is inserted between doubly coupled neurons \(A\) and \(B\). From the physical structure neuron \(C\) is directly regulated by neuron \(A\) and indirectly regulated by neuron \(B\). Its discharge sequence and the \(PSF\) distribution are shown in Figures 5 and 6. Figure 5 is a discharge sequence for three motif models. Its analysis method is similar to that of two motif models. However, in Figure 5, the discharge sequence diagrams of neurons with structural links (neuron \(A\) and neuron \(B\)) and without structural links (neuron \(B\) and neuron \(C\)) are simulated, respectively. It can be seen from Figure 5 that there is a certain difference in the pulse sequence between neuron \(A\) and neuron \(B\), but their  
Figure 5: The discharge sequence of three neurons connecting model 1(b-2). Figure 6: PSF distribution diagram of three neurons model 1(b-2) in different connection States. discharge activities are regular and consistent. Although there is no structural link between neuron \(B\) and neuron \(C\), there is a phase synchronization state in the discharge sequence, which is consistent with the theoretical analysis. This shows that the synchronization state between neurons is an important means of neural information transmission. Therefore, it can be shown from Figure 5 that there is an effective transmission between neuron \(B\) and neuron \(C\) in the process of information transmission; synchronization characteristics can build dynamic effective links between neurons and these effective links do not necessarily correspond to structural links one by one, which may be the main reason for flexible path switching in brain networks. Figure 6 is a boxplot of the three Motif models. It also conducted 100 simulation experiments, and the statistical analysis concluded that the \(PSF\) values between neurons \(C\to A\to B\to C\) are relatively stable. The \(PSF\) value is maintained between \([0.3,\ 0.4]\). Under this structure, the phase information of the stimulus signal has a certain promoting effect on the synchronous state, thus resulting in a \"new\" connected pathway \(BC\). The simulation results show that there is an effective pathway between the neuronal nodes, that the synchronization between the neural nodes can be regulated by the phase offset of the stimulus signal and that the degree of regulation depends on the size of the \(PSF\) value. Under the model structure of Figure 1(b-2), it also considers the effect of time delay on \(PSF\). The simulation results are shown in Figure 7. The value range of delay is \([0,\ 160]\). Through the analysis of the simulation results, it is found that, compared with the two neuron structure links, the \(PSF\) of Figure 1(b-2) model is lower. It is maintained between [0.28, 0.36] and there is a weak fluctuation phenomenon with the increase in time delay, indicating that the time delay also has a certain effect under this structure. In addition, the reason for the small change trend of \(PSF\) is that the increase in the number of central nodes affects the transmission of nerve impulses in the whole link, and the signal is annihilated in the bottom noise of the nervous system in the process of transmission due to the increase in the number of nodes.