A linear model for characterization of synchronization frequencies of neural networks

The synchronization frequency of neural networks and its dynamics have important roles in deciphering the working mechanisms of the brain. It has been widely recognized that the properties of functional network synchronization and its dynamics are jointly determined by network topology, network connection strength, i.e., the connection strength of different edges in the network, and external input signals, among other factors. However, mathematical and computational characterization of the relationships between network synchronization frequency and these three important factors are still lacking. This paper presents a novel computational simulation framework to quantitatively characterize the relationships between neural network synchronization frequency and network attributes and input signals. Specifically, we constructed a series of neural networks including simulated small-world networks, real functional working memory network derived from functional magnetic resonance imaging, and real large-scale structural brain networks derived from diffusion tensor imaging, and performed synchronization simulations on these networks via the Izhikevich neuron spiking model. Our experiments demonstrate that both of the network synchronization strength and synchronization frequency change according to the combination of input signal frequency and network self-synchronization frequency. In particular, our extensive experiments show that the network synchronization frequency can be represented via a linear combination of the network self-synchronization frequency and the input signal frequency. This finding could be attributed to an intrinsically-preserved principle in different types of neural systems, offering novel insights into the working mechanism of neural systems.