Izhikevich neuronal model is based on the modeling of cortical and thalamic neurons. This model has the characteristics of being closer to the discharge properties of real biological neurons and it is convenient for large-scale simulation. A square neural network composed of 200 × 200 Izhikevich neurons is constructed under random boundary conditions in this paper, the computer simulation method is used to calculate the spatiotemporal characteristics and synchronization factor of the square network, and the firing patterns and bifurcation phenomena of neurons, as well as the spatiotemporal patterns and synchronization properties of the square network are studied. The results show that in the square neural network constructed by Izhikevich neurons with different discharge modes under the same current stimulation and coupling intensity, the emergence and disappearance of spiral wave seeds can be observed in the neural network only when the neurons are in the Regular Spiking discharge mode. On the other hand, spiral wave seeds cannot be observed in the square neural network constructed by Izhikevich neurons with other discharge modes (e.g. Fast Spiking, Chattering, Internally Bursting). When the external current stimulation is constant, only the medium-sized coupling strength between neurons can induce the emergence and extinction of spiral wave seeds in the square neural network, and smaller or larger coupling strength cannot induce spiral wave seeds in the neural network. In addition, the synchronization factor in square neural networks has been investigated.