Noise-induced pattern formation and synchronization in a square-lattice neuronal network

Effects of noise on the collective dynamic phenomena such as patterns and firing synchronization are studied in a square-lattice FitzHughNagumo neural network with gap junctions. It is shown that as the noise intensity is above a critical value, typical patterns can emerge and propagate through the network in the form of coexisting circular waves and parallel ones with spatially periodic structure. Circular waves can change from a single-array to double-array as the noise increases. Furthermore, we can observe that spatial evolutions of patterns can exhibit different styles as the noise is changed. In addition, we study noise-induced firing synchronization of neurons. In particular, firing synchronization can be enhanced, and then can reach a saturated value as the noise is large enough. More interestingly, it is found that the stronger the coupling strength is, the larger the noise intensity is needed to make neurons fire. Finally, the critical relation between the noise intensity and the coupling strength is given to investigate the occurrence of firing synchronization in the network.