Various effects induced by local synchronization in neural networks

In the cerebral cortex, the large-scale synchronous firing of neurons can cause epilepsy, during which spiral waves can spontaneously occur. The relationship between the synchronous firing of a large number of neurons and the spontaneous generation of spiral waves is still unclear. In this paper, a two-dimensional neuronal network with the long-range coupling regions generated by adding long-range horizontal connections is constructed. The Morris-Lecar neuron model is used to study the propagation of waves in the two-dimensional neuronal network with the rectangular long-range coupling regions. Numerical simulation results show that the plan and target waves whose propagation directions are both parallel to that of the long-range coupling can lead the neurons to be excited synchronously in the long-range coupling region. This synchronous firing is accompanied by delayed firing of some neurons and premature firing of others. When the width of the long-range coupling region exceeds the critical width, all the neurons in the long-range coupling region delay firing. When the width of the long-range coupling region exceeds a maximum conduction width, the waves will not pass through the long-range coupling region. When the size of the rectangular region of the long-range coupling is selected appropriately, the synchronous excitation of neurons can cause network to present the backfiring effect and to have the selectivity of wave propagation direction. Furthermore, the selectivity of wave propagation direction is very sensitive to whether the neuron is in the stationary state and also to the change of coupling strength, so that the high frequency plane wave train can partially pass through the long-range coupling region whose width exceeds the maximum conduction width. So we can control whether the wave can pass through the long-range coupling region of a certain width by giving the neurons in the long-range coupling region a tiny perturbation. When one or two long-range coupling regions are constructed in the neural network and the size of the long-range coupling regions is selected appropriately, the self-sustaining plane wave, spiral wave and target wave can appear spontaneously in the network when the wave passes through the long-range coupling regions. The physical mechanisms behind those phenomena are also analyzed.