Pattern formation induced by gradient field coupling in bi-layer neuronal networks

Abstract

The pattern formation in heterogeneous excitable media is a common phenomenon for spatiotemporal systems. In this paper, a bi-layer neuronal network is studied in which the two layers are connected using electromagnetic field coupling with two types of coupling gradients (i.e., step-like and cone-like). It is observed that when the central intensity of a gradient fieid is small, cone-like has less destructive effect on the target wave of the first layer compared to step-like. To further study the influence of environmental factors on pattern formation, the central intensity and external stimulation in the gradient field are continuously increased. The results show that the larger central intensity of the gradient field destroys the the target wave of the first layer and may form a spiral wave, and a larger external stimulation is more effective for inducing spiral waves in the second layer. Finally, synchronization factors are used to predict the pattern and formation mechanism of the spiral wave, and it is found that spiral waves are more likely to occur at the second layer with smaller values and the opposite at the first layer.