Frequency synchronization and excitabilities of two coupled heterogeneous Morris-Lecar neurons

•Two coupling heterogeneous neurons can exhibit frequency locking and even complete frequency.•The class-3 neuron in a two-neuron motif can produce various excitabilities, including tonic- and phasic-spiking.•There exists a diversity of the dynamic path to the same neuronal excitabilities. It is well-known that neurons in the same cortical region still have highly heterogeneous responses. These different intrinsic neuronal features play an important role in the connection and coding of the biological nervous system. In this work, we study the response dynamics of a two-neuron network motif composed of class-1 and class-3 Morris-Lecar neurons under an external directional current. The two neurons were found to exhibit frequency locking and then undergo complete frequency synchronization with increases in the coupling strength and the input current. The class-3 neuron in the motif can produce various excitabilities with appropriate coupling strength and input current, including tonic- and phasic-spiking, not only single-spiking. Extensive bifurcation analysis revealed that class-3 neurons undergo different dynamic routes even for the same excitability, and vice versa. These results provide insight into collective behaviors and firing characteristics in heterogeneous neuronal networks.