How time-delayed coupling influences differential feedback control of bursting synchronization in modular neuronal network

The nontrivial influence of time-delayed coupling on differential feedback control of bursting synchronization is explored in modular neuronal network. Numerical simulations show that collective rhythm of bursting synchronization, irrespective of the numbers of subnetworks, can appear when the considered modular network is forced by large coupling. Then, a control domain of effective synchronization suppression is detected when the proposed differential feedback control is applied to suppress bursting synchronization. Furthermore, time delay in the coupling is introduced, and how it affects differential feedback control to inhibit bursting synchronization is explored. The result declares that small time delay can enhance differential feedback control to suppress bursting synchronization, and there exists an optimal time delay such that this enhancement can obtain its maximum. This presented result is expected to facilitate us to suppress bursting synchronization in realistic neuronal networks.