Complete dynamical analysis of a neocortical network model

The brain is a complex system consisting of a large number of interacting neurons. Recently, a simple nonlinear biological model has been proposed for the up and down state transitions in the network of excitatory and inhibitory neurons. In this paper, we study the dynamical behavior of this model by calculating the Lyapunov exponents and bifurcation diagrams for various values of synaptic connections. We show that varying the synaptic strength values has a considerable effect on the bifurcations in the model. Furthermore, we show that the model can exhibit chaotic firing for certain values of the excitatory-excitatory synaptic strength.