Robust synchronization of bursting Hodgkin–Huxley neuronal systems coupled by delayed chemical synapses

• A modified HH neuronal model which exhibits bursting behaviors by incorporating a slow calcium ionic channel into traditional HH neuron model is proposed.
• A two-neuron system coupled by a delayed chemical synapse is constructed and the synchronization properties of the system, with the synapse being excitatory and inhibitory, are explored respectively.
• A globally coupled neuronal network with delayed inhibitory chemical synapses is set up and the effects of synaptic conductance, synaptic delay and synaptic decay time on synchronization and oscillation frequency of the whole network are checked.

Synchronized firing of bursting neurons has been found in many real neural systems. In this paper, a modified bursting Hodgkin–Huxley neuronal model is proposed and used to construct neuronal systems with heterogeneous neurons coupled by delayed chemical synapses, then synchronization of the systems is studied in various conditions. First, synchronization for a two-neuron system is explored. It is found that if the synapse is excitatory, the two neurons could achieve burst synchronization easily. If the synapse is inhibitory, they can achieve anti-phase burst synchronization, which is robust to variation of systematic parameters. Second, robust synchronization for a globally coupled neuronal network is investigated. It is found that the robustness of the synchronization is sensitive to the parameter values of synaptic conductance and synaptic delay, but is less sensitive to the parameter values of synaptic decay time. It is also found that the oscillation frequency of the whole network is sensitive to the parameter values of synaptic delay and synaptic decay time, but is less sensitive to the parameter value of synaptic conductance.