Synchronous firing transition between different regions of brain neural networks enhanced by Hamiltonian energy

In this paper, we investigate the energy evolution dynamics and regulation mechanics of firing patterns in neural networks. We construct a four-region coupled neurons network by considering the connectivity matrix based on the cat brain cortical link matrix. To observe the laws and characteristics of the evolution of the firing patterns with the network energy, which is injected into the network through an external stimulation current. It is found that, on one hand, when neurons in the network are all in a resting state, if the external energy with appropriate frequency is introduced from the visual area, it not only can induce the neurons in their own area to start oscillating, but also the neuron cells in the other three regions can gradually oscillate with the increase of the signal energy intensity. On the other hand, when external stimuli are applied into the four regions separately, different frequencies of external signals can individually induce oscillation in the corresponding regions, this suggesting that different functional regions could generate selective responses to different external stimulus signals. In specially, when the energy exceeds a certain values, such synchronous oscillations in single regions will rapidly spread throughout the region, resulting in abnormal hyper-synchronous oscillations across the whole brain networks. Our results hope to further understand the law of the energy evolution in the brain neural network and the mechanism of epilepsy caused by hyper-synchronous abnormal discharge.