Stability of coupled excitatory-inhibitory neural populations and application to control of multi-stable systems

The hierarchy of models of interacting neural populations with excitatory and inhibitory connections is described using second-order nonlinear ordinary differential equations. Systematic analytical and numerical studies are aimed at determining stability conditions of the coupled system. Generalized stability conditions are derived for a class of excitatory-inhibitory neural population models. Equilibrium continuation analysis is applied to interpret the obtained stability conditions. The results are discussed in the context of chaotic brain dynamics theory and chaotic itinerancy. Attractor switching in biologically relevant multi-stable systems is demonstrated.