Delayed feedback control of bursting synchronization in small-world neuronal networks

Neuronal networks in some areas of the brain cortex present the small-world property. We investigate the delayed feedback control of bursting synchronization in small-world neuronal networks. Without control, a transition to mutual synchronization takes place on the bursting time scale of coupled neurons, while on the spiking time scale, they behave asynchronously. It is shown that the synchronization of small-world neuronal networks is greatly enhanced by a large fraction of shortcuts, but saturates when it exceeds a critical value. We investigate the suppression of such synchronized activity of the neuron population using a linear delayed feedback control. Domains of effective synchronization suppression are depicted in terms of feedback strength and time delay. We get that the overall efficiency of synchronization suppression of a small-world network is much higher than for global coupling and scale-free populations with the same initial synchronization strength. Considering that some pathological conditions are related with the synchronization of bursting neurons in the brain, the presented results could have important implications for the application of time-delayed feedback in the deep brain stimulation.

► We study the transition to bursting synchronization in small-world neural networks.
► We suppress the synchronized bursting activity using linear delayed feedback control.
► Small-world network is more effective for synchronization suppression.