Applied Mathematics and Computation
The combination of chemical, physical, electrical, and structural properties of the neurons has made them highly complex dynamical units. One of the best tools to deal with such high-level complexity is to study the neural spatiotemporal patterns. In this work, we have focused specifically on the spiral spatiotemporal pattern. Spirals make an important contribution to some of the cortical activities. However, they also may misregulate the neural activities and lead to neurological disorders such as epilepsy or attention deficit hyperactivity disorder. Here, we have studied the effect of amplitude and frequency of an external force on the dynamics of the spiral wave in one- and two-layer neural network. We have also examined the role of synaptic connections between the neurons. For each examination, three modes of zero-, low-, and high-frequency external magnetic induction are considered. In the one-layer neural network with low frequency magnetic excitation, the frequency of the stimuli overtakes the stimuli amplitude and significantly changes the dynamics of the spirals. Nonetheless, in the case of high-frequency magnetic induction, neither the amplitude nor the frequency of the electrical force have control over the existing spirals. We also have shown how the timely pattern of neural synchronization changes when the neurons are allowed to more communicate with one another. In the two-layer neural network, on the other hand, we have shown that both the amplitude and frequency of the electrical stimuli can help to control or even eliminate the spiral waves.