<p>Based on a modified four-dimensional Hindmarsh-Rose neuron model, the chemical synapse coupled neuronal system is constructed. The effects of different parameters on the bifurcation and synchronization of the coupled system are studied. Matcant software is used to determine the type of equilibrium point and Hopf bifurcation point. It is found that the system generates subcritical Hopf bifurcation with the change of parameters, and the hidden dynamics behavior near the subcritical Hopf bifurcation point is discussed. Based on the bifurcation theory, the effects of single and multiple parameters on the firing pattern, bifurcation, and synchronization of the coupled neuron system are studied. It is concluded that the coupled neuron system can generate periodic firing, inverse period-doubling discharge, and chaotic cluster discharge under different parameter values. This paper also compares and analyzes the synchronization state of the coupled system before and after adding time lag. Moreover, it is found that a certain time lag can destroy and delay the synchronization state of the coupled neural system. Using the synchronization factor statistic, the synchronous behavior and existence of chimera states of coupled neural network systems are studied, which will provide useful clues to reveal the underlying mechanisms of information encoding and transmission processes in complex neural systems.</p>