Transitions between irregular and rhythmic firing patterns in excitatory-inhibitory neuronal networks

Changes in firing patterns are an important hallmark of the functional status of neuronal networks. We apply dynamical systems methods to understand transitions between irregular and rhythmic firing in an excitatory-inhibitory neuronal network model. Using the geometric theory of singular perturbations, we systematically reduce the full model to a simpler set of equations, one that can be studied analytically. The analytic tools are used to understand how an excitatory-inhibitory network with a fixed architecture can generate both activity patterns for possibly different values of the intrinsic and synaptic parameters. These results are applied to a recently developed model for the subthalamopallidal network of the basal ganglia. The results suggest that an increase in correlated activity, corresponding to a pathological state, may be due to an increased level of inhibition from the striatum to the inhibitory GPe cells along with an increased ability of the excitatory STN neurons to generate rebound bursts.