Parameter-dependent synchronization transition of coupled neurons with co-existing spiking and bursting

• Synchronizations in two coupled neurons with co-existing behaviors are simulated.
• One neuron is spiking and the other the co-existing bursting.
• Synchronization behaviors are dependent on the parameter values.
• The behaviors include the synchronization states and transition procedures.
• The relationship between the attraction domain and synchronizations is discussed.

A firing pattern transition is simulated in the Leech neuron model, firstly from bursting to co-existence of spiking and bursting and then to spiking. The attraction domain of spiking and bursting for three different parameter values are calculated. Synchronization transition processes of two coupled Leech neurons, one is bursting and the other the co-existing spiking, are simulated for the three parameters. The three synchronization processes appear similar as the coupling strength increases, beginning from non-synchronization to complete synchronization through a complex dynamical procedure, but their detailed processes are different depending on the parameter values. The transition procedure is complex and the complete synchronization is in bursting for larger parameter values, while the process is simple with complete synchronization of spiking for smaller values. The potential relationship between complete synchronization and the attraction domain is also discussed. The results are instructive to understanding the synchronization behaviors of the coupled neuronal system with co-existing attractors.