Synaptic changes modulate spontaneous transitions between tonic and bursting neural activities in coupled Hindmarsh-Rose neurons

Experimentally, certain cells in the brain exhibit a spike-burst activity with burst synchronization at transition to and during sleep (or drowsiness), while they demonstrate a desynchronized tonic activity in the waking state. We herein investigated the neural activities and their transitions by using a model of coupled Hindmarsh-Rose neurons in an Erd\ifmmode \mbox{\H{o}}\else \H{o}\fi{}s-R\'enyi random network. By tuning synaptic strength, spontaneous transitions between tonic and bursting neural activities can be realized. With excitatory chemical synapses or electrical synapses, slow-wave activity (SWA) similar to that observed during sleep can appear, as a result of synchronized bursting activities. SWA cannot appear in a network that is dominated by inhibitory chemical synapses, because neurons exhibit desynchronized bursting activities. Moreover, we found that the critical synaptic strength related to the transitions of neural activities depends only on the network average degree (i.e., the average number of signals that all the neurons receive). We demonstrated, both numerically and analytically, that the critical synaptic strength and the network average degree obey a power-law relation with an exponent of $\ensuremath{-}1$. Our study provides a possible dynamical network mechanism of the transitions between tonic and bursting neural activities for the wakefulness-sleep cycle, and of the SWA during sleep. Further interesting and challenging investigations are briefly discussed as well.