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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.