Dynamics of a Cortical Neural Network Based on a Simple Model

The collective dynamics of a randomly connected neuronal network motivated by the anatomy of a mammalian cortex based on a simple model are studied. This simple model can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. By varying some key parameters, such as the connection weights of neurons, the external current injection and the noise of intensity, this neuronal network will exhibit various collective behaviors. It is demonstrated that the synchronization status of the neuronal network has a strong relationship with the key parameters and the external current has more influence on the spiking of inhibitory neurons than that of excitatory neurons. These results may be instructive in understanding the collective dynamics of a mammalian cortex.