This work considers networks of two nodes with bidirectionally and unidirectionally linear coupling. Each node is represented by a system of ordinary differential equations of FitzHugh-Nagumo type which is obtained by simplifying the famous Hodgkin-Huxley model. From two network topologies, the existence of global attractors, and the sufficient condition under the coupling strength are sought such that the synchronization phenomenon occurs. The result shows that the network with bidirectionally linear coupling synchronizes more easily than the other. The paper also shows this theoretical result numerically and see that there is a compromise.