Bursting synchronization in clustered neuronal networks

Neuronal networks in the brain exhibit the modular （clustered） property, i.e., they are composed of certain subnetworks with differential internal and external connectivity. We investigate bursting synchronization in a clustered neuronal network. A transition to mutual-phase synchronization takes place on the bursting time scale of coupled neurons, while on the spiking time scale, they behave asynchronously. This synchronization transition can be induced by the variations of inter- and intra coupling strengths, as well as the probability of random links between different subnetworks. Considering that some pathological conditions are related with the synchronization of bursting neurons in the brain, we analyze the control of bursting synchronization by using a time-periodic external signal in the clustered neuronal network, Simulation results show a frequency locking tongue in the driving parameter plane, where bursting synchronization is maintained, even in the presence of external driving. Hence, effective synchronization suppression can be realized with the driving parameters outside the frequency locking region.

Synchronization and bursting transition of the coupled Hindmarsh-Rose systems with asymmetrical time-delays

The study of synchronization and bursting transition is very important and valuable in cognitive activities and action control of brain as well as enhancement for the reliability of the cortex synapses. However, we wonder how the synaptic strength and synaptic delay, especially the asymmetrical time-delays between different neurons can collectively influence their synchronous firing behaviors. In this paper, based on the Hindmarsh-Rose neuronal systems with asymmetrical time-delays, we investigate the collective effects of various delays and coupling strengths on the synchronization and bursting transition. It is shown that the interplay between delay and coupling strength can not only enhance or destroy the synchronizations but also can induce the regular transitions of bursting firing patterns. Specifically, as the coupling strength or time-delay increasing, the firing patterns of the time-delayed coupling neuronal systems consistently present a regular transition, that is, the periods of spikes during the bursting firings increase firstly and then decrease slowly. In particular, in contrast to the case of symmetrical time-delays,asymmetrical time-delays can lead to the paroxysmal synchronizations of coupling neuronal systems, as well as the concentration level of synchronization for the non-identically coupled system is superior to the one of identical coupling. These results more comprehensively reveal the rich nonlinear dynamical behaviors of neuronal systems and may be helpful for us to have a better understanding of the neural coding.