Synchronization provides an effective way for stable signal exchange and balance in membrane potentials of neurons. Both electric synapse and chemical synapse play important role in processing signals by emitting signal and receiving signals, and the encoded signals are estimated by a variety of synaptic currents. For two or more neurons, the synaptic current can pass along the coupling channels with feasible self-adaption and then synaptic plasticity is formed. The occurrence of synaptic currents generates complex biophysical effect because continuous propagation and pumping of calcium, sodium and potassium can induce time-varying physical field intra- and extracellular of cell. Indeed, the field effect becomes more distinct when more neurons are involved in a functional region of the nervous system. To decrease the energy consumption and obtain fast signal exchange, autonomic learning is often activated to select the most appropriate coupling gain in the synapses connected to neurons. That is, synapse can increase the synaptic intensity carefully before reaching synchronization. In this paper, the two-variable Fitzhugh-Nagumo neuron driven by voltage source is used to investigate the synchronization stability when hybrid synapse is applied between two neurons. By using the saturation gain method, the synapse intensity is increased with appropriate step until synchronization is reached, and then the coupling intensity is fixed to find the threshold for stabilizing complete synchronization. It gives new clues to understand the synaptic plasticity from physical viewpoint. © 2019 Elsevier Ltd