Nonlinear delayed feedback control for effective desynchronization of small-world neural networks

The topology of the neural network in brain cortex exhibits small-world characteristics. Excessive synchronization of the brain neuron population is believed to play the crucial role in the emergence of the neuropsychological disorders such as Parkinson´s disease and epilepsy, so it is significant to investigate how to eliminate these pathological rhythmic brain activities. A small-world network composed of map-based neurons is presented, which can get chaotic bursting synchronization when the coupling strength exceeds a certain threshold. When nonlinear delayed feedback signal is applied into the network, a complete desynchronization is achieved and neuron´s inherent bursting characteristic is restored. Desynchronization by this method is robust against parameter variations.