Transitions to synchronization induced by synaptic increasing in coupled tonic neurons with electrical synapses

Experimental evidence had suggested that the net synaptic strength of nervous system increases during wakefulness. By using a model of coupled tonic neurons, we studied transitions to synchronization induced by synaptic increasing. Our findings revealed that in the presence of electrical synapses, synaptic increasing initially leads to a transition from desynchronized tonic activity (DTA) to desynchronized bursting activity (DBA). This DBA then transitions towards bursting activity with burst synchronization (BABS), followed by bursting activity with spike synchronization (BASS). As the synaptic strength continues to increase, there is a transition from BASS to approximately synchronized tonic activity (ASTA) once the synaptic strength reaches a critical value. Finally, completely synchronized tonic activity (CSTA) emerges when the synaptic strength reaches another critical value. Notably, the values of these two critical synaptic strengths, for ASTA and CSTA respectively, depend solely on the absolute value of the second largest eigenvalue of network coupling matrix. Through numerical and analytical methods, we demonstrated that both of these critical values and the absolute value of the eigenvalue follow a power-law relationship with exponent −1. These results suggested that the transitions to synchronization driven by synaptic increasing are a multi-time-scale phenomenon consisting of six stages: DTA, DBA, BABS, BASS, ASTA, and CSTA. We also briefly discussed the meaningful implications of sleep deprivation and the further challenging investigations that arise from these findings.