Synchronization In A Small World Neural Network Based On Map Model

There are about 1011 neurons in the brain cortex, and these neurons connect with others through synapses to construct the neural network and realize a variety of physiological functions of the brain. The topology of the neural network in brain exhibits small-world property, and pathologically strong synchronization of the brain neurons population is believed to play the crucial role in the emergence of the nerve diseases 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 was presented in this paper to investigate the chaotic bursting synchronization of neural system. Moreover, we analyze how the effect of external periodic driving signal and the nonlinear delayed feedback on the synchronization of the network.Firstly, we analyse the bursting synchronization in the small-world network composed of map-based neurons. We use average field, bursting frequency and order parameter as the diagnostic parameters to study the relationship between bursting synchronization and topology of the network, such as the coupling strength, rewiring probability and size of the network.Secondly, a external periodic signal is applied to the bursting synchronized neural network to research how the amplitude and frequency of the external periodic signal affect the external chaotic phase synchronization of network. Through numerical simulation, we find that the width of the frequency locking interval varies with the network size, rewiring probability and the number of the driven neurons. It is demonstrated that there exists an optimal small-world topology, resulting in the largest peak value of frequency locking interval in the parameter plane. We infer that the externally applied driving parameters outside the frequency locking region can effectively suppress pathologically synchronized rhythms of bursting neurons in the brain.Finally, a nonlinear delayed feedback signal is applied to the neural network to study the desynchronization effect by adjusting the nonlinear feedback strength and delay time. When nonlinear delayed feedback signal was applied into the network, a complete desynchronization was achieved and neuron’s intrinsic bursting characteristic was restored. Compared with the linear delayed feedback control, desynchronization by nonlinear delayed feedback was robust against parameter variations.In this paper, the effect of external periodic signal and delayed feedback signal on the synchronization is revealed based on the dynamics analysis of a small-world network composed of map-based neurons. It provides a new idea for the treatment of neurologic disease caused by pathological synchronization.